Bibliography. of Ut -.1 ( u) = 0, Indiana Univ. Math. J. 30 (1981), pp

Size: px
Start display at page:

Download "Bibliography. of Ut -.1 ( u) = 0, Indiana Univ. Math. J. 30 (1981), pp"

Transcription

1 Bibliography [1] R. Adams, Sobolev Spaces, Academic Press, New York (1975). [2] L. V. Alfors, Lectures on quasiconformal mappings, Wadsworth & Brooks/ Cole, Monterey CA (1987). [3] D. Andreucci, A priori bounds for weak solutions of the filtration equation, SIAM J. Math. Anal. 22 # 1 (1991), pp [4] D. Andreucci and E. DiBenedetto, A new approach to initial traces in nonlinear filtration, Ann. Inst. H. Poincare Analyse non Lineaire, 7 # 4 (1990), pp [5] S.N. Antonsev, Axially symmetric problems of gas dynamics with free boundaries, Doklady Akad. Nauk SSSR 216 # 3 (1974), pp [6] D.G. Aronson and L.A. Caffarelli, The initial trace of a solution of the porous medium equation, Trans. AMS 280 # 1 (1983), pp [7] D.G. Aronson and J. Serrin, Local behaviour of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal. 25 (1967), pp [8] G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mech. 16 (1952), pp [9] Ph. Benilan and M.G. Crandall, The continuous dependence on of solutions of Ut -.1 ( u) = 0, Indiana Univ. Math. J. 30 (1981), pp [10] Ph. Benilan, M.G. Crandall and M. Pierre, Solutions of the porous medium medium equation in RN under optimal conditions on initial values, Indiana Univ. Math. J. 33 (1984), pp [11] Ph. Benilan and T. Gallouet (personal communication).

2 382 Bibliography [12] S.N. Bernstein, Collected works. III Differential equations, calculus ofvariations and geometry (/ ), Izdat. Akad. Nauk SSSR, Moscow (1960) (Russian). [13] J.G.Berryman, Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundaries, J. Math. Phys. 18 # 11 (1977), pp [14] J.G. Berryman and C.J. Holland, Stability of the separable solution for fast diffusion equation, Arch. Rational Mech. Anal. 74 (1980), pp [15] L. Boccardo and T. Gallouet, Non linear elliptic and parabolic equations involving measure data, (to appear). [16] L. Boccardo, F. Murat and J.P. Puel, VXJ estimates for some non linear elliptic partial differential equations and applications to an existence result, SIAM J. Math. Anal. [17] B. Bojarski and T. Iwaniec, p-harmonic equations and quasiregular Mappings, Inst. Angew. Universimt Bonn (preprint 1983). [18] H. Brezis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl. 62 (1983), pp [19] H. Brezis, Elliptic equations with limiting Sobolev exponents-the impact of topology, Comm. Pure Appl. Math. XXXIX (1986), SI7-S39. [20] L.A. Caffarelli and L.C. Evans, Continuity of the temperature in the two phase Stefan problem, Arch. Rational Mech. Anal. 81 (1983), pp [21] L.A. Caffarelli and A. Friedman, Regularity of the free-boundary of a gas in a n-dimensional porous medium, Indiana Univ. Math. J. 29, (1980), pp [22] S. Campanato, Equazioni ellittiche del [[0 ordine e spazi {,2,>., Ann. Math. Pura Appl. 69 (1965), pp [23] S. Campanato, Equazioni paraboliche del secondo ordine e spazi {,p,8 ( n, 0), Ann. Math. Pura Appl. 73 (1966), pp [24] Y.Z. Chen, HOlder estimates for solutions of uniformly degenerate quasilinear parabolic equations, Chin. Ann. Math. 5B (4) (1984), pp [25] Y.Z. Chen, HOlder continuity of the gradients of solutions of non-linear degenerate parabolic systems, Acta Math. Sinica, New Series 2 # 4 (1986), pp [26] Y.Z. Chen and E. DiBenedetto, On the local behaviour of solutions of singular parabolic equations, Arch. Rational Mech. Anal. 103 # 4 (1988), pp [27] Y.Z. Chen and E. DiBenedetto, Boundary estimates for solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math. 395 (1989), pp [28] Y.Z. Chen and E. DiBenedetto, HOlder estimates of solutions of singular parabolic equations with measurable coefficients, Arch. Rational Mech. Anal. 118 (1992), pp

3 Bibliography 383 [29] Y.Z. Chen and E. DiBenedetto, On the Harnack inequality for non-negative solutions of singular parabolic equations, Proc. of Conf. Non-linear diffusion, in Honour of J. Serrin, Minneapolis May [30] H. Choe, HOlder regularity for the gradient of solutions of certain singular parabolic equations, Comm. Part. Diff. Equations 16 # 11 (1991), pp [31] H. Choe, HOlder continuity of solutions of certain degenerate parabolic systems, Non-linear Anal. 8 # 3 (1992), pp [32] G. DaPrato, Spazi.c(p,(}) (fl, 8) e loro propriem, Ann. Math. Pura Appl. 69 (1965), pp [33] E. DeGiorgi, Sulla differenziabilita' e l'analiticita' delle estremali degli integrali multipli regolari, Mem. Acc. Sci. Torino, Cl. Sc. Fis. Mat. Nat. (3) 3 (1957), pp [34] E. DiBenedetto, Continuity of weak solutions to certain singular parabolic equations, Ann.Mat. Puta Appl. 4 # 130 (1982), pp [35] E. DiBenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 # 1 (1983), pp [36] E. DiBenedetto and A. Friedman, Regularity of solutions of non-linear degenerate parabolic systems, J. Reine Angew. Math. 349 (1984), pp [37] E. DiBenedetto and A. Friedman, HOlder estimates for non-linear degenerate parabolic systems, J. Reine Angew. Math. 357 (1985), pp [38] E. DiBenedetto, A boundary modulus of continuity for a class of singular parabolic equations, J. Diff. Equations 6 # 3 (1986), pp [39] E. DiBenedetto, On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients, Ann. Sc. Norm. Sup. Pisa Cl. Sc. Serie IV, XIII 3 (1986), [40] E. DiBenedetto, Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations, Arch. Rational Mech. Anal. 100 # 2 (1988), pp [41] E. DiBenedetto and M.A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation Trans. AMS 314 (1989), pp [42] E. DiBenedetto and M.A. Herrero, Non negative solutions ofthe evolution p-laplacian equation. Initial traces and Cauchy problem when 1 < p < 2, Arch. Rational Mech. Anal. 111 # 3 (1990), pp [43] E. DiBenedetto, Y. C. Kwong and V. Vespri, Local space analiticity of solutions of certain singular parabolic equations, Indiana Univ. Math. J. 40 # 2 (1991), pp [44] E. DiBenedetto and Y.c. Kwong, Intrinsic Harnack estimates and extinction profile for certain singular parabolic equations, Trans AMS 330 # 2 (1992), pp

4 384 Bibliography [45] E. DiBenedetto, J. Manfredi and V. Vespri, Boundary gradient bounds for evolution p-iaplacian equations. Proc. Int. Conf. of Evolution Equations and their Ground States, Gregynog, Wales, 1989 [46] E. DiBenedetto, J. Manfredi, On the local behaviour of solutions of degenerate elliptic systems, Amer. J. Math. (to appear) [47] B. Fuglede, A criterion of non-vanishing differential of a smooth map, Bull. London Math. Soc. 14 (1982), pp [48] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. Math. Studies 105, Princeton Univ. Press., Princeton N.J. (1983). [49] M. Giaquinta and E. Giusti, Global c1,a -regularity for second order quasilinear elliptic equations in divergence form, J. Reine Angew. Math. # 351 (1984), pp [50] J. Hadamard, Extension Ii l'equation de la chaleur d'un theoreme de A Harnack, Rend. Circ. Mat. Palermo Ser. 23 (1954), pp [51] AM. Il'in, AS. Kalashnikov and O.A. Oleinik, Linear equations of second order of parabolic type, Uspeki Matern. NAUK, 17 # 3 (1962), pp [52] A.V. Ivanov, Uniform Holder estimates for generalized solutions of quasilinear parabolic equations admitting a double degeneracy, Algebra Anal. 3 # 2 (1991), pp [53] A.V.Ivanov, The classes Bml and HOlder estimates for quasilinear doubly degenerate parabolic equations. Zap. Nauchn. Sem. St. Petersburg Otdel. Math. Inst. Steklov (LOMI) 197 (1992), pp (Engl. transl: J. Soviet Math.). [54] AV. Ivanov and P.Z. Mkrtchen, On the regularity up to the boundary of weak solutions of the first initial-boundary value problem for quasilinear doubly degenerate parabolic equations. Zap. Nauchn. Sem. St. Petersburg, Otdel. Math. Inst. Steklov (LOM!) 196 (1991), pp [55] T. Iwaniec, Projections onto gradient fields and LP-estimates for degenerate elliptic equations. Studia Math. 75 (1983), pp [56] D.O. Joseph, D.A Nield and G. Papanicolau, Non linear equations governing flow in a saturated porous medium (preprint). [57] AS. Kalashnikov, On a heat conduction equation for a medium with nonuniformly distributed non-linear heat sources or absorbers, Bull. Univ. Moscow, Math. Mech. 3 (1983), pp [58] AS. Kalashnikov, Cauchy's problem in classes of increasing functions for certain quasi -linear degenerate parabolic equations of the second order, Diff. Uravneniya 9 # 4 (1973), [59] AS. Kalashnikov, On uniqueness conditions for the generalized solutions of the Cauchy problem for a class of quasi-linear degenerate parabolic equations, Diff. Uravneniya 9 # 12 (1973),

5 Bibliography 385 [60] S.N. Kruzkov, On the apriori estimation of solutions of linear parabolic equations and of solutions of boundary value problems for a certain class of quasi-linear parabolic equations, Dokl. Akad. NAUK SSSR # 138 (1961), pp (Engl. transl.: Soviet Math. Dokl. # 2 (1961), pp ). [61] S.N. Kruzkov, A priori estimates and certain properties of the solutions of elliptic and parabolic equations of second order, Mat. Sbornik 65 # 107 (1964), pp (Engl. trans.: Amer. Math. Soc. Transl. 2 # 68 (1968), pp ). [62] S.N. Kruzkov, Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications, Math. Zametki 6 (1969), pp (Russian). [63] N.V. Krylov, Non-linear elliptic and parabolic equations of the second order. D. Reidel, Dordrecht, Holland (1987). [64] N. V. Krylov and M. V. Safonov, A certain property of solutions of parabolic equations with measurable coefficients, Math. USSR lzvestijia 16 # 1 (1981), pp [65] O.A. Ladyzenskaja, New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc. Steklov lnst. Math. # 102 (1967), pp (English transl.: Trudy Math. lnst. Steklov # 102 (1967), pp ). [66] O.A. Ladyzenskaja, and N.N. Ural'tzeva, Linear and quasilinear elliptic equations, Academic Press, New York (1968). [67] O.A. Ladyzenskaja, V.A. Solonnikov andn.n. Ural'tzeva, Linear and quasilinear equations of parabolic type. Transl. Math. Mono. Vol. 23 AMS, Providence, RI (1968). [68] a.m. Lieberman, The first initial-boundary value problem for quasilinear second order parabolic equations, Ann. Scuola Norm. Sup. Pisa 13 (1986), pp [69] a.m. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Non-linear Anal. 12 (1988), pp [70] a.m. Lieberman, Boundary and initial regularity for solutions of degenerate parabolic equations, Nonlinear Anal. TMA 20 (1993), pp (to appear). [71] a.m. Lieberman, Mean oscillation estimates and HOlder regularity for the gradients of solutions of degenerate parabolic systems (to appear). [72] Lin Fan Hua, Boundary C 1,f3 -regularity of p-harmonic functions (preprlnt 1988). [73] J.L. Lions, Quelques methodes de resolution des problemes aux limites nonlineaires. Dunod, Paris (1969). [74] L.K. Martinson and K.B. Paplov, The effect of magnetic plasticity in non Newtonian fluids, Magnit. Gidrodinamika 3 (1969), pp

6 386 Bibliography [75] L.K. Martinson and K.B. Paplov, Unsteady shear flows of a conducting fluid with a rheological power law, Magnit. Gidrodinamika # 2 (1970), pp [76] V.G. Mazja, Sobolev Spaces. Springer-Verlag, New York, (1985). [77] M. Meier, Boundedness and integrability properties of weak solutions of quasilinear elliptic systems. J. Reine Angew. Math. 333 (1982), pp [78] G. Minty, Monotone (non-linear) operators in Hilbert spaces, Duke Math. J. 29 (1962), pp [79] C.B. Morrey, Multiple integrals in the calculus of variations. Springer Verlag, New York, (1966). [80] C.B. Morrey, Partial regularity results for non-linear elliptic systems. J. Math. Mech. 17 (1968), pp [81] J. Moser, A new proof of DeGiorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), pp [82] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), pp [83] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), pp [84] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), pp [85] M. Pierre, Uniqueness of the solutions of Ut - Ll ( u) = 0 with initial datum a measure, Nonlin. Anal. 6, # 2 (1987), pp [86] B. Pini, Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico, Rend. Sem. Math. Univ. Padova 23 (1954), pp [87] M. Porzio, A priori bounds for weak solutions of certain degenerate parabolic equations, Nonlin. Anal. 20, # 11 (1991), pp. 1093, [88] M. Porzio and V. Vespri, HOlder estimates for local solutions of some doubly non-linear degenerate parabolic equations, J. Diff. Equ. (to appear). [89] Y.G. Resetniak, Mappings with bounded distorsion in space. 'Nauka' Novosibirski, Moscow (1982) (Russian). [90] P.E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal. 7 (1983), pp [91] M.V. Safonov, The Harnack inequality for elliptic equations and the HOlder continuity of their solutions, Boundary problems of mathematical physics and adjacent questions in the theory offunctions, Zap. Nauchn. Sem. Leningrad Otdel. Math. Inst. Steklov (LaM!) 96 (1980), pp (Engl. transl.: J. Soviet Math. (LOMI) 20 (1983), pp ). [92] J. Serrin, Local behaviour of solutions of quasilinear elliptic equations, Acta Math. 111 (1964), pp

7 Bibliography 387 [93] G. Stampacchia, Equations elliptiques du second ordre a coefficients discontinues. sem. Math. Sup. 16, Les Presses de l'universite de Montreal, Montreal (1966). [94] S. Tacklind, Sur les classes quasianalitiques des solutions des equations aux derivee partielles du type parabolique, Acta Reg. Soc. Sc. Uppsaliensis (Ser. 4) 10, # 3 (1936), pp [95] P. Tolksdorff, Everywhere regularity for some quasi-linear systems with lack of ellipticity, Ann. Mat. Pura Appl. 4 # 134 (1983), pp [96] N.S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic partial differential equations, Comm. Pure Appl. Math. 20 (1967), pp [97] N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), pp [98] A.N. Tychonov, 1'heoremes d'unicite pour l'equation de la chaleur Math. Sbomik 42 (1935), pp [99] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), pp [100] N.N. Ural'tceva, Degenerate quasilinear elliptic systems, Zap. Nauk. Sem. Leningrad Otdel. Math. Inst. Steklov # 7 (1968), pp (Russian). [101] V. Vespri, L oo estimates for non-linear parabolic equations with natural growth conditions, Rend. Sem. Mat. Univ. Padova (in press). [102] V. Vespri, On the local behaviour of a certain class of doubly non-linear parabolic equations, Manuscripta Math. 75 (1992), pp [103] V. Vespri, Harnack type inequalities for solutions of certain doubly nonlinear parabolic equations. J. Math. Anal. Appl. (in press). [104] M. Wiegner, On en-regularity of the gradient of solutions of degenerate parabolic systems, Ann. Mat. Pura Appl. 4 # 145 (1986), pp [105] D.V. Widder, Positive temperatures in an infmite rod, Trans. AMS, # 55 (1944), pp

References

References References 1. A. Abbott, Cell Biology: Hopping Fences, Nature, 433, (2005), 680 683. 2. E. Acerbi, G. Mingione and G. Seregin, Regularity results for parabolic systems related to a class of non-newtonian

More information

ON THE NATURAL GENERALIZATION OF THE NATURAL CONDITIONS OF LADYZHENSKAYA AND URAL TSEVA

ON THE NATURAL GENERALIZATION OF THE NATURAL CONDITIONS OF LADYZHENSKAYA AND URAL TSEVA PATIAL DIFFEENTIAL EQUATIONS BANACH CENTE PUBLICATIONS, VOLUME 27 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WASZAWA 1992 ON THE NATUAL GENEALIZATION OF THE NATUAL CONDITIONS OF LADYZHENSKAYA

More information

EXISTENCE AND REGULARITY RESULTS FOR SOME NONLINEAR PARABOLIC EQUATIONS

EXISTENCE AND REGULARITY RESULTS FOR SOME NONLINEAR PARABOLIC EQUATIONS EXISTECE AD REGULARITY RESULTS FOR SOME OLIEAR PARABOLIC EUATIOS Lucio BOCCARDO 1 Andrea DALL AGLIO 2 Thierry GALLOUËT3 Luigi ORSIA 1 Abstract We prove summability results for the solutions of nonlinear

More information

Recent developments in elliptic partial differential equations of Monge Ampère type

Recent developments in elliptic partial differential equations of Monge Ampère type Recent developments in elliptic partial differential equations of Monge Ampère type Neil S. Trudinger Abstract. In conjunction with applications to optimal transportation and conformal geometry, there

More information

ANNALES DE L I. H. P., SECTION C

ANNALES DE L I. H. P., SECTION C ANNALES DE L I. H. P., SECTION C E. DI BENEDETTO NEIL S. TRUDINGER Harnack inequalities for quasi-minima of variational integrals Annales de l I. H. P., section C, tome 1, n o 4 (1984), p. 295-308

More information

Continuity of Solutions of Linear, Degenerate Elliptic Equations

Continuity of Solutions of Linear, Degenerate Elliptic Equations Continuity of Solutions of Linear, Degenerate Elliptic Equations Jani Onninen Xiao Zhong Abstract We consider the simplest form of a second order, linear, degenerate, divergence structure equation in the

More information

Universität des Saarlandes. Fachrichtung 6.1 Mathematik

Universität des Saarlandes. Fachrichtung 6.1 Mathematik Universität des Saarlandes U N I V E R S I T A S S A R A V I E N I S S Fachrichtung 6.1 Mathematik Preprint Nr. 207 The elastic-plastic torsion problem: a posteriori error estimates for approximate solutions

More information

Nonlinear aspects of Calderón-Zygmund theory

Nonlinear aspects of Calderón-Zygmund theory Ancona, June 7 2011 Overture: The standard CZ theory Consider the model case u = f in R n Overture: The standard CZ theory Consider the model case u = f in R n Then f L q implies D 2 u L q 1 < q < with

More information

REGULARITY AND COMPARISON PRINCIPLES FOR p-laplace EQUATIONS WITH VANISHING SOURCE TERM. Contents

REGULARITY AND COMPARISON PRINCIPLES FOR p-laplace EQUATIONS WITH VANISHING SOURCE TERM. Contents REGULARITY AND COMPARISON PRINCIPLES FOR p-laplace EQUATIONS WITH VANISHING SOURCE TERM BERARDINO SCIUNZI Abstract. We prove some sharp estimates on the summability properties of the second derivatives

More information

Review: Stability of Bases and Frames of Reproducing Kernels in Model Spaces

Review: Stability of Bases and Frames of Reproducing Kernels in Model Spaces Claremont Colleges Scholarship @ Claremont Pomona Faculty Publications and Research Pomona Faculty Scholarship 1-1-2006 Review: Stability of Bases and Frames of Reproducing Kernels in Model Spaces Stephan

More information

Universität des Saarlandes. Fachrichtung 6.1 Mathematik

Universität des Saarlandes. Fachrichtung 6.1 Mathematik Universität des Saarlandes U N I V E R S I T A S S A R A V I E N I S S Fachrichtung 6.1 Mathematik Preprint Nr. 155 A posteriori error estimates for stationary slow flows of power-law fluids Michael Bildhauer,

More information

COMPARISON PRINCIPLES FOR CONSTRAINED SUBHARMONICS PH.D. COURSE - SPRING 2019 UNIVERSITÀ DI MILANO

COMPARISON PRINCIPLES FOR CONSTRAINED SUBHARMONICS PH.D. COURSE - SPRING 2019 UNIVERSITÀ DI MILANO COMPARISON PRINCIPLES FOR CONSTRAINED SUBHARMONICS PH.D. COURSE - SPRING 2019 UNIVERSITÀ DI MILANO KEVIN R. PAYNE 1. Introduction Constant coefficient differential inequalities and inclusions, constraint

More information

ON THE REGULARITY OF WEAK SOLUTIONS OF THE 3D NAVIER-STOKES EQUATIONS IN B 1

ON THE REGULARITY OF WEAK SOLUTIONS OF THE 3D NAVIER-STOKES EQUATIONS IN B 1 ON THE REGULARITY OF WEAK SOLUTIONS OF THE 3D NAVIER-STOKES EQUATIONS IN B 1, A. CHESKIDOV AND R. SHVYDKOY ABSTRACT. We show that if a Leray-Hopf solution u to the 3D Navier- Stokes equation belongs to

More information

An Introduction to Second Order Partial Differential Equations Downloaded from Bibliography

An Introduction to Second Order Partial Differential Equations Downloaded from  Bibliography Bibliography [1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1965. [2] F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy, 81 (3) 1973, 637-654.

More information

SOME RECENT RESULTS ON THE EQUATION OF PRESCRIBED GAUSS CURVATURE

SOME RECENT RESULTS ON THE EQUATION OF PRESCRIBED GAUSS CURVATURE 215 SOME RECENT RESULTS ON THE EQUATION OF PRESCRIBED GAUSS CURVATURE John I.E. Urbas In this article we discuss some recently established results concerning convex solutions u E c 2 (Q) of the equation

More information

A Product Property of Sobolev Spaces with Application to Elliptic Estimates

A Product Property of Sobolev Spaces with Application to Elliptic Estimates Rend. Sem. Mat. Univ. Padova Manoscritto in corso di stampa pervenuto il 23 luglio 2012 accettato l 1 ottobre 2012 A Product Property of Sobolev Spaces with Application to Elliptic Estimates by Henry C.

More information

PRINCIPALI PUBBLICAZIONI DI MARIA AGOSTINA VIVALDI

PRINCIPALI PUBBLICAZIONI DI MARIA AGOSTINA VIVALDI PRINCIPALI PUBBLICAZIONI DI MARIA AGOSTINA VIVALDI 1) Absolutely minimizing Lipschitz extensions and infinity harmonic functions on the Sierpinski gasket. Nonlinear Anal. 163 (2017), 71-85. In collaborazione

More information

THE HARNACK INEQUALITY FOR -HARMONIC FUNCTIONS. Peter Lindqvist and Juan J. Manfredi

THE HARNACK INEQUALITY FOR -HARMONIC FUNCTIONS. Peter Lindqvist and Juan J. Manfredi Electronic Journal of ifferential Equations Vol. 1995(1995), No. 04, pp. 1-5. Published April 3, 1995. ISSN 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp (login: ftp) 147.26.103.110

More information

Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent Yūki Naito a and Tokushi Sato b a Department of Mathematics, Ehime University, Matsuyama 790-8577, Japan b Mathematical

More information

arxiv: v1 [math.ap] 27 Nov 2014

arxiv: v1 [math.ap] 27 Nov 2014 Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension Boris Haspot arxiv:1411.7679v1 [math.ap] 27 Nov 214 Abstract We prove weak-strong

More information

Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains

Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains Ilaria FRAGALÀ Filippo GAZZOLA Dipartimento di Matematica del Politecnico - Piazza L. da Vinci - 20133

More information

Selected References on the p-laplacian and related topics in quasilinear elliptic PDE

Selected References on the p-laplacian and related topics in quasilinear elliptic PDE Selected References on the p-laplacian and related topics in quasilinear elliptic PDE Yuanji Cheng, Juan J. Manfredi May 10, 2005 Books & lecture notes 1. H. Aikava, M Essén, Akawa, Potential theory selected

More information

Heat equations with singular potentials: Hardy & Carleman inequalities, well-posedness & control

Heat equations with singular potentials: Hardy & Carleman inequalities, well-posedness & control Outline Heat equations with singular potentials: Hardy & Carleman inequalities, well-posedness & control IMDEA-Matemáticas & Universidad Autónoma de Madrid Spain enrique.zuazua@uam.es Analysis and control

More information

arxiv: v1 [math.ap] 10 May 2013

arxiv: v1 [math.ap] 10 May 2013 0 SOLUTIOS I SOM BORDRLI CASS OF LLIPTIC QUATIOS WITH DGRAT CORCIVITY arxiv:1305.36v1 [math.ap] 10 May 013 LUCIO BOCCARDO, GISLLA CROC Abstract. We study a degenerate elliptic equation, proving existence

More information

Some aspects of vanishing properties of solutions to nonlinear elliptic equations

Some aspects of vanishing properties of solutions to nonlinear elliptic equations RIMS Kôkyûroku, 2014, pp. 1 9 Some aspects of vanishing properties of solutions to nonlinear elliptic equations By Seppo Granlund and Niko Marola Abstract We discuss some aspects of vanishing properties

More information

Institute of Mathematics, Russian Academy of Sciences Universitetskiĭ Prosp. 4, Novosibirsk, Russia

Institute of Mathematics, Russian Academy of Sciences Universitetskiĭ Prosp. 4, Novosibirsk, Russia PARTIAL DIFFERENTIAL EQUATIONS BANACH CENTER PUBLICATIONS, VOLUME 27 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WARSZAWA 1992 L p -THEORY OF BOUNDARY VALUE PROBLEMS FOR SOBOLEV TYPE EQUATIONS

More information

ON THE EXISTENCE OF CONTINUOUS SOLUTIONS FOR NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS WITH STRONGLY GROWING LOWER-ORDER TERMS

ON THE EXISTENCE OF CONTINUOUS SOLUTIONS FOR NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS WITH STRONGLY GROWING LOWER-ORDER TERMS ROCKY MOUNTAIN JOURNAL OF MATHMATICS Volume 47, Number 2, 2017 ON TH XISTNC OF CONTINUOUS SOLUTIONS FOR NONLINAR FOURTH-ORDR LLIPTIC QUATIONS WITH STRONGLY GROWING LOWR-ORDR TRMS MYKHAILO V. VOITOVYCH

More information

Elliptic & Parabolic Equations

Elliptic & Parabolic Equations Elliptic & Parabolic Equations Zhuoqun Wu, Jingxue Yin & Chunpeng Wang Jilin University, China World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI Contents Preface v

More information

arxiv: v2 [math.ap] 6 Sep 2007

arxiv: v2 [math.ap] 6 Sep 2007 ON THE REGULARITY OF WEAK SOLUTIONS OF THE 3D NAVIER-STOKES EQUATIONS IN B 1, arxiv:0708.3067v2 [math.ap] 6 Sep 2007 A. CHESKIDOV AND R. SHVYDKOY ABSTRACT. We show that if a Leray-Hopf solution u to the

More information

arxiv: v1 [math.ap] 27 May 2010

arxiv: v1 [math.ap] 27 May 2010 A NOTE ON THE PROOF OF HÖLDER CONTINUITY TO WEAK SOLUTIONS OF ELLIPTIC EQUATIONS JUHANA SILJANDER arxiv:1005.5080v1 [math.ap] 27 May 2010 Abstract. By borrowing ideas from the parabolic theory, we use

More information

arxiv: v1 [math.ap] 18 Jan 2019

arxiv: v1 [math.ap] 18 Jan 2019 manuscripta mathematica manuscript No. (will be inserted by the editor) Yongpan Huang Dongsheng Li Kai Zhang Pointwise Boundary Differentiability of Solutions of Elliptic Equations Received: date / Revised

More information

Existence of the free boundary in a diffusive ow in porous media

Existence of the free boundary in a diffusive ow in porous media Existence of the free boundary in a diffusive ow in porous media Gabriela Marinoschi Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest Existence of the free

More information

Weights, inequalities and a local HÖlder norm for solutions to ( / t-l)(u)=divf on bounded domains

Weights, inequalities and a local HÖlder norm for solutions to ( / t-l)(u)=divf on bounded domains Weights, inequalities and a local HÖlder norm for solutions to ( / t-l)(u)=divf on bounded domains CAROLINE SWEEZY Department of Mathematical Sciences New Mexico State University Las Cruces, New Mexico

More information

GRAND SOBOLEV SPACES AND THEIR APPLICATIONS TO VARIATIONAL PROBLEMS

GRAND SOBOLEV SPACES AND THEIR APPLICATIONS TO VARIATIONAL PROBLEMS LE MATEMATICHE Vol. LI (1996) Fasc. II, pp. 335347 GRAND SOBOLEV SPACES AND THEIR APPLICATIONS TO VARIATIONAL PROBLEMS CARLO SBORDONE Dedicated to Professor Francesco Guglielmino on his 7th birthday W

More information

Regularity estimates for fully non linear elliptic equations which are asymptotically convex

Regularity estimates for fully non linear elliptic equations which are asymptotically convex Regularity estimates for fully non linear elliptic equations which are asymptotically convex Luis Silvestre and Eduardo V. Teixeira Abstract In this paper we deliver improved C 1,α regularity estimates

More information

Growth estimates through scaling for quasilinear partial differential equations

Growth estimates through scaling for quasilinear partial differential equations Growth estimates through scaling for quasilinear partial differential equations Tero Kilpeläinen, Henrik Shahgholian, and Xiao Zhong March 5, 2007 Abstract In this note we use a scaling or blow up argument

More information

HARNACK INEQUALITY FOR NONDIVERGENT ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS. Seick Kim

HARNACK INEQUALITY FOR NONDIVERGENT ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS. Seick Kim HARNACK INEQUALITY FOR NONDIVERGENT ELLIPTIC OPERATORS ON RIEMANNIAN MANIFOLDS Seick Kim We consider second-order linear elliptic operators of nondivergence type which are intrinsically defined on Riemannian

More information

Weak Solutions to Nonlinear Parabolic Problems with Variable Exponent

Weak Solutions to Nonlinear Parabolic Problems with Variable Exponent International Journal of Mathematical Analysis Vol. 1, 216, no. 12, 553-564 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ijma.216.6223 Weak Solutions to Nonlinear Parabolic Problems with Variable

More information

September 7, :49 WSPC/INSTRUCTION FILE Schikorra-Shieh- Spector-fractional-p-Laplace-CCM-revision

September 7, :49 WSPC/INSTRUCTION FILE Schikorra-Shieh- Spector-fractional-p-Laplace-CCM-revision REGULARITY FOR A FRACTIONAL p-laplace EQUATION ARMIN SCHIKORRA Mathematisches Institut, Abt. für Reine Mathematik, Albert-Ludwigs-Universität, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany armin.schikorra@math.uni-freiburg.de

More information

Nonlinear Diffusion and Free Boundaries

Nonlinear Diffusion and Free Boundaries Nonlinear Diffusion and Free Boundaries Juan Luis Vázquez Departamento de Matemáticas Universidad Autónoma de Madrid Madrid, Spain V EN AMA USP-São Carlos, November 2011 Juan Luis Vázquez (Univ. Autónoma

More information

GEOMETRIC TANGENTIAL ANALYSIS AND SHARP REGULARITY FOR DEGENERATE PDES EDUARDO V. TEIXEIRA AND JOSÉ MIGUEL URBANO

GEOMETRIC TANGENTIAL ANALYSIS AND SHARP REGULARITY FOR DEGENERATE PDES EDUARDO V. TEIXEIRA AND JOSÉ MIGUEL URBANO Pré-Publicações do Departamento de Matemática Universidade de Coimbra Preprint Number 18 37 GEOMETRIC TANGENTIAL ANALYSIS AND SHARP REGULARITY FOR DEGENERATE PDES EDUARDO V. TEIXEIRA AND JOSÉ MIGUEL URBANO

More information

4) D. Giachetti, E. Mascolo Spectral properties of a class of quasi-elliptic operators, Ann. Univ. Ferrara Sez. VII (N.S.) 25 (1979),

4) D. Giachetti, E. Mascolo Spectral properties of a class of quasi-elliptic operators, Ann. Univ. Ferrara Sez. VII (N.S.) 25 (1979), PUBLICATIONS ARTICLES ON JOURNALS 1 ) D. Giachetti, E. Mascolo Quasi-elliptic problems in Sobolev weighted spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 63 (1977), n. 5, 360-367.

More information

A CONNECTION BETWEEN A GENERAL CLASS OF SUPERPARABOLIC FUNCTIONS AND SUPERSOLUTIONS

A CONNECTION BETWEEN A GENERAL CLASS OF SUPERPARABOLIC FUNCTIONS AND SUPERSOLUTIONS A CONNECTION BETWEEN A GENERAL CLASS OF SUPERPARABOLIC FUNCTIONS AND SUPERSOLUTIONS RIIKKA KORTE, TUOMO KUUSI, AND MIKKO PARVIAINEN Abstract. We show to a general class of parabolic equations that every

More information

COINCIDENCE SETS IN THE OBSTACLE PROBLEM FOR THE p-harmonic OPERATOR

COINCIDENCE SETS IN THE OBSTACLE PROBLEM FOR THE p-harmonic OPERATOR PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 95, Number 3, November 1985 COINCIDENCE SETS IN THE OBSTACLE PROBLEM FOR THE p-harmonic OPERATOR SHIGERU SAKAGUCHI Abstract. We consider the obstacle

More information

Renormalized Solutions of a Nonlinear Parabolic Equation with Double Degeneracy

Renormalized Solutions of a Nonlinear Parabolic Equation with Double Degeneracy Electronic Journal of Qualitative Theory of Differential Equations 26, No. 5, -2; http://www.math.u-szeged.hu/ejqtde/ Renormalized Solutions of a Nonlinear Parabolic Equation with Double Degeneracy Zejia

More information

b i (µ, x, s) ei ϕ(x) µ s (dx) ds (2) i=1

b i (µ, x, s) ei ϕ(x) µ s (dx) ds (2) i=1 NONLINEAR EVOLTION EQATIONS FOR MEASRES ON INFINITE DIMENSIONAL SPACES V.I. Bogachev 1, G. Da Prato 2, M. Röckner 3, S.V. Shaposhnikov 1 The goal of this work is to prove the existence of a solution to

More information

BLOW-UP AND EXTINCTION OF SOLUTIONS TO A FAST DIFFUSION EQUATION WITH HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

BLOW-UP AND EXTINCTION OF SOLUTIONS TO A FAST DIFFUSION EQUATION WITH HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS Electronic Journal of Differential Equations, Vol. 016 (016), No. 36, pp. 1 10. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu BLOW-UP AND EXTINCTION OF SOLUTIONS TO A FAST

More information

A RIEMANN PROBLEM FOR THE ISENTROPIC GAS DYNAMICS EQUATIONS

A RIEMANN PROBLEM FOR THE ISENTROPIC GAS DYNAMICS EQUATIONS A RIEMANN PROBLEM FOR THE ISENTROPIC GAS DYNAMICS EQUATIONS KATARINA JEGDIĆ, BARBARA LEE KEYFITZ, AND SUN CICA ČANIĆ We study a Riemann problem for the two-dimensional isentropic gas dynamics equations

More information

The Harnack inequality for second-order elliptic equations with divergence-free drifts

The Harnack inequality for second-order elliptic equations with divergence-free drifts The Harnack inequality for second-order elliptic equations with divergence-free drifts Mihaela Ignatova Igor Kukavica Lenya Ryzhik Monday 9 th July, 2012 Abstract We consider an elliptic equation with

More information

On the high regularity of solutions to the p-laplacian boundary value problem in exterior domains

On the high regularity of solutions to the p-laplacian boundary value problem in exterior domains On the high regularity of solutions to the p-laplacian boundary value problem in exterior domains Francesca Crispo, Carlo Romano Grisanti, Paolo Maremoti Published in ANNALI DI MATEMATICA PURA E APPLICATA,

More information

Lecture No 2 Degenerate Diffusion Free boundary problems

Lecture No 2 Degenerate Diffusion Free boundary problems Lecture No 2 Degenerate Diffusion Free boundary problems Columbia University IAS summer program June, 2009 Outline We will discuss non-linear parabolic equations of slow diffusion. Our model is the porous

More information

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR PARABOLIC OPERATORS OF LERAY-LIONS TYPE AND MEASURE DATA

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR PARABOLIC OPERATORS OF LERAY-LIONS TYPE AND MEASURE DATA ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR PARABOLIC OPERATORS OF LERAY-LIONS TYPE AND MEASURE DATA FRANCESCO PETITTA Abstract. Let R N a bounded open set, N 2, and let p > 1; we study the asymptotic behavior

More information

On non negative solutions of some quasilinear elliptic inequalities

On non negative solutions of some quasilinear elliptic inequalities On non negative solutions of some quasilinear elliptic inequalities Lorenzo D Ambrosio and Enzo Mitidieri September 28 2006 Abstract Let f : R R be a continuous function. We prove that under some additional

More information

HARNACK S INEQUALITY FOR GENERAL SOLUTIONS WITH NONSTANDARD GROWTH

HARNACK S INEQUALITY FOR GENERAL SOLUTIONS WITH NONSTANDARD GROWTH Annales Academiæ Scientiarum Fennicæ Mathematica Volumen 37, 2012, 571 577 HARNACK S INEQUALITY FOR GENERAL SOLUTIONS WITH NONSTANDARD GROWTH Olli Toivanen University of Eastern Finland, Department of

More information

ON THE UNIQUENESS IN THE 3D NAVIER-STOKES EQUATIONS

ON THE UNIQUENESS IN THE 3D NAVIER-STOKES EQUATIONS ON THE UNIQUENESS IN THE 3D NAVIER-STOKES EQUATIONS Abdelhafid Younsi To cite this version: Abdelhafid Younsi. ON THE UNIQUENESS IN THE 3D NAVIER-STOKES EQUATIONS. 4 pages. 212. HAL Id:

More information

J. Kinnunen and R. Korte, Characterizations of Sobolev inequalities on metric spaces, arxiv: v2 [math.ap] by authors

J. Kinnunen and R. Korte, Characterizations of Sobolev inequalities on metric spaces, arxiv: v2 [math.ap] by authors J. Kinnunen and R. Korte, Characterizations of Sobolev inequalities on metric spaces, arxiv:79.197v2 [math.ap]. 28 by authors CHARACTERIZATIONS OF SOBOLEV INEQUALITIES ON METRIC SPACES JUHA KINNUNEN AND

More information

A LOWER BOUND FOR THE GRADIENT OF -HARMONIC FUNCTIONS Edi Rosset. 1. Introduction. u xi u xj u xi x j

A LOWER BOUND FOR THE GRADIENT OF -HARMONIC FUNCTIONS Edi Rosset. 1. Introduction. u xi u xj u xi x j Electronic Journal of Differential Equations, Vol. 1996(1996) No. 0, pp. 1 7. ISSN 107-6691. URL: http://ejde.math.swt.edu (147.6.103.110) telnet (login: ejde), ftp, and gopher access: ejde.math.swt.edu

More information

ONE-DIMENSIONAL PARABOLIC p LAPLACIAN EQUATION. Youngsang Ko. 1. Introduction. We consider the Cauchy problem of the form (1.1) u t = ( u x p 2 u x

ONE-DIMENSIONAL PARABOLIC p LAPLACIAN EQUATION. Youngsang Ko. 1. Introduction. We consider the Cauchy problem of the form (1.1) u t = ( u x p 2 u x Kangweon-Kyungki Math. Jour. 7 (999), No. 2, pp. 39 50 ONE-DIMENSIONAL PARABOLIC p LAPLACIAN EQUATION Youngsang Ko Abstract. In this paper we establish some bounds for solutions of parabolic one dimensional

More information

Note on the Chen-Lin Result with the Li-Zhang Method

Note on the Chen-Lin Result with the Li-Zhang Method J. Math. Sci. Univ. Tokyo 18 (2011), 429 439. Note on the Chen-Lin Result with the Li-Zhang Method By Samy Skander Bahoura Abstract. We give a new proof of the Chen-Lin result with the method of moving

More information

ON A CONJECTURE OF P. PUCCI AND J. SERRIN

ON A CONJECTURE OF P. PUCCI AND J. SERRIN ON A CONJECTURE OF P. PUCCI AND J. SERRIN Hans-Christoph Grunau Received: AMS-Classification 1991): 35J65, 35J40 We are interested in the critical behaviour of certain dimensions in the semilinear polyharmonic

More information

A duality variational approach to time-dependent nonlinear diffusion equations

A duality variational approach to time-dependent nonlinear diffusion equations A duality variational approach to time-dependent nonlinear diffusion equations Gabriela Marinoschi Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania A duality variational

More information

i. Bonic R. and Frampton J., Differentiable functions on certain Banach spaces, Bull. Amer. Math. Soc. 71(1965),

i. Bonic R. and Frampton J., Differentiable functions on certain Banach spaces, Bull. Amer. Math. Soc. 71(1965), References i. Bonic R. and Frampton J., Differentiable functions on certain Banach spaces, Bull. Amer. Math. Soc. 71(1965), 393-395. 2. Cameron R. H. and Graves R., Additive functionals on a space of continuous

More information

Uniqueness of ground states for quasilinear elliptic equations in the exponential case

Uniqueness of ground states for quasilinear elliptic equations in the exponential case Uniqueness of ground states for quasilinear elliptic equations in the exponential case Patrizia Pucci & James Serrin We consider ground states of the quasilinear equation (.) div(a( Du )Du) + f(u) = 0

More information

Journal of Inequalities in Pure and Applied Mathematics

Journal of Inequalities in Pure and Applied Mathematics Journal of Inequalities in Pure and Applied Mathematics http://jipam.vu.edu.au/ Volume 3, Issue 3, Article 46, 2002 WEAK PERIODIC SOLUTIONS OF SOME QUASILINEAR PARABOLIC EQUATIONS WITH DATA MEASURES N.

More information

Extremal Solutions and Instantaneous Complete Blow-up for Elliptic and Parabolic Problems

Extremal Solutions and Instantaneous Complete Blow-up for Elliptic and Parabolic Problems Extremal Solutions and Instantaneous Complete Blow-up for Elliptic and Parabolic Problems Xavier Cabré ICREA and Universitat Politècnica de Catalunya Departament de Matemàtica Aplicada 1 Diagonal 647.

More information

arxiv: v2 [math.ap] 10 Mar 2016

arxiv: v2 [math.ap] 10 Mar 2016 Hölder gradient estimates for parabolic homogeneous p-laplacian equations arxiv:1505.05525v2 [math.ap] 10 Mar 2016 Tianling Jin and Luis Silvestre March 11, 2016 Abstract We prove interior Hölder estimates

More information

Proc. A. Razmadze Math. Inst. 151(2009), V. Kokilashvili

Proc. A. Razmadze Math. Inst. 151(2009), V. Kokilashvili Proc. A. Razmadze Math. Inst. 151(2009), 129 133 V. Kokilashvili BOUNDEDNESS CRITERION FOR THE CAUCHY SINGULAR INTEGRAL OPERATOR IN WEIGHTED GRAND LEBESGUE SPACES AND APPLICATION TO THE RIEMANN PROBLEM

More information

A GENERALIZATION OF THE FLAT CONE CONDITION FOR REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS

A GENERALIZATION OF THE FLAT CONE CONDITION FOR REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 100, Number 2. June 1987 A GENERALIZATION OF THE FLAT CONE CONDITION FOR REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS GARY M. LIEBERMAN ABSTRACT.

More information

A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth

A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth E. DiBenedetto 1 U. Gianazza 2 C. Klaus 1 1 Vanderbilt University, USA 2 Università

More information

REGULARITY OF GENERALIZED NAVEIR-STOKES EQUATIONS IN TERMS OF DIRECTION OF THE VELOCITY

REGULARITY OF GENERALIZED NAVEIR-STOKES EQUATIONS IN TERMS OF DIRECTION OF THE VELOCITY Electronic Journal of Differential Equations, Vol. 00(00), No. 05, pp. 5. ISSN: 07-669. UR: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu REGUARITY OF GENERAIZED NAVEIR-STOKES

More information

On critical Fujita exponents for the porous medium equation with a nonlinear boundary condition

On critical Fujita exponents for the porous medium equation with a nonlinear boundary condition J. Math. Anal. Appl. 286 (2003) 369 377 www.elsevier.com/locate/jmaa On critical Fujita exponents for the porous medium equation with a nonlinear boundary condition Wenmei Huang, a Jingxue Yin, b andyifuwang

More information

Large time behavior of solutions of the p-laplacian equation

Large time behavior of solutions of the p-laplacian equation Large time behavior of solutions of the p-laplacian equation Ki-ahm Lee, Arshak Petrosyan, and Juan Luis Vázquez Abstract We establish the behavior of the solutions of the degenerate parabolic equation

More information

HAMILTON-JACOBI EQUATIONS : APPROXIMATIONS, NUMERICAL ANALYSIS AND APPLICATIONS. CIME Courses-Cetraro August 29-September COURSES

HAMILTON-JACOBI EQUATIONS : APPROXIMATIONS, NUMERICAL ANALYSIS AND APPLICATIONS. CIME Courses-Cetraro August 29-September COURSES HAMILTON-JACOBI EQUATIONS : APPROXIMATIONS, NUMERICAL ANALYSIS AND APPLICATIONS CIME Courses-Cetraro August 29-September 3 2011 COURSES (1) Models of mean field, Hamilton-Jacobi-Bellman Equations and numerical

More information

LORENTZ SPACE ESTIMATES FOR VECTOR FIELDS WITH DIVERGENCE AND CURL IN HARDY SPACES

LORENTZ SPACE ESTIMATES FOR VECTOR FIELDS WITH DIVERGENCE AND CURL IN HARDY SPACES - TAMKANG JOURNAL OF MATHEMATICS Volume 47, Number 2, 249-260, June 2016 doi:10.5556/j.tkjm.47.2016.1932 This paper is available online at http://journals.math.tku.edu.tw/index.php/tkjm/pages/view/onlinefirst

More information

AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS. To the memory of our friend and colleague Fuensanta Andreu

AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS. To the memory of our friend and colleague Fuensanta Andreu AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS JUAN J. MANFREDI, MIKKO PARVIAINEN, AND JULIO D. ROSSI Abstract. We characterize p-harmonic functions in terms of an asymptotic mean value

More information

AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS

AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-harmonic FUNCTIONS JUAN J. MANFREDI, MIKKO PARVIAINEN, AND JULIO D. ROSSI Abstract. We characterize p-harmonic functions in terms of an asymptotic mean value

More information

Fachrichtung 6.1 Mathematik

Fachrichtung 6.1 Mathematik Universität des Saarlandes U N I V E R S I T A S S A R A V I E N I S S Fachrichtung 6.1 Mathematik Preprint Nr. A note on splitting-type variational problems with subquadratic growth Dominic reit Saarbrücken

More information

Global regularity of a modified Navier-Stokes equation

Global regularity of a modified Navier-Stokes equation Global regularity of a modified Navier-Stokes equation Tobias Grafke, Rainer Grauer and Thomas C. Sideris Institut für Theoretische Physik I, Ruhr-Universität Bochum, Germany Department of Mathematics,

More information

to appear in Nonlinear Analysis TMA (special issue for Enzo Mitidieri s birthday) HARNACK INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS

to appear in Nonlinear Analysis TMA (special issue for Enzo Mitidieri s birthday) HARNACK INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS to appear in Nonlinear Analysis TMA (special issue for Enzo Mitidieri s birthday) HARNACK INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS PAOLO BARONI, MARIA COLOMBO, AND GIUSEPPE MINGIONE Abstract. We prove

More information

A comparison theorem for nonsmooth nonlinear operators

A comparison theorem for nonsmooth nonlinear operators A comparison theorem for nonsmooth nonlinear operators Vladimir Kozlov and Alexander Nazarov arxiv:1901.08631v1 [math.ap] 24 Jan 2019 Abstract We prove a comparison theorem for super- and sub-solutions

More information

Seong Joo Kang. Let u be a smooth enough solution to a quasilinear hyperbolic mixed problem:

Seong Joo Kang. Let u be a smooth enough solution to a quasilinear hyperbolic mixed problem: Comm. Korean Math. Soc. 16 2001, No. 2, pp. 225 233 THE ENERGY INEQUALITY OF A QUASILINEAR HYPERBOLIC MIXED PROBLEM Seong Joo Kang Abstract. In this paper, e establish the energy inequalities for second

More information

A Nonlinear PDE in Mathematical Finance

A Nonlinear PDE in Mathematical Finance A Nonlinear PDE in Mathematical Finance Sergio Polidoro Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna (Italy) polidoro@dm.unibo.it Summary. We study a non

More information

arxiv: v1 [math.ap] 21 Dec 2016

arxiv: v1 [math.ap] 21 Dec 2016 arxiv:1612.07051v1 [math.ap] 21 Dec 2016 On the extension to slip boundary conditions of a Bae and Choe regularity criterion for the Navier-Stokes equations. The half-space case. H. Beirão da Veiga, Department

More information

SOME PROBLEMS OF SHAPE OPTIMIZATION ARISING IN STATIONARY FLUID MOTION

SOME PROBLEMS OF SHAPE OPTIMIZATION ARISING IN STATIONARY FLUID MOTION Advances in Mathematical Sciences and Applications Vol., No. (200x), pp. Gakkōtosho Tokyo, Japan SOME PROBLEMS OF SHAPE OPTIMIZATION ARISING IN STATIONARY FLUID MOTION Luigi. Berselli Dipartimento di Matematica

More information

arxiv: v1 [math.ap] 28 Mar 2014

arxiv: v1 [math.ap] 28 Mar 2014 GROUNDSTATES OF NONLINEAR CHOQUARD EQUATIONS: HARDY-LITTLEWOOD-SOBOLEV CRITICAL EXPONENT VITALY MOROZ AND JEAN VAN SCHAFTINGEN arxiv:1403.7414v1 [math.ap] 28 Mar 2014 Abstract. We consider nonlinear Choquard

More information

SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze

SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze CARLO SBORDONE New estimates for div-curl products and very weak solutions of PDEs Annali della Scuola Normale Superiore di Pisa, Classe

More information

SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze

SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze NORMAN G. MEYERS An L p -estimate for the gradient of solutions of second order elliptic divergence equations Annali della Scuola Normale

More information

K-DIMENSIONAL NONLOCAL BOUNDARY-VALUE PROBLEMS AT RESONANCE. 1. Introduction In this article we study the system of ordinary differential equations

K-DIMENSIONAL NONLOCAL BOUNDARY-VALUE PROBLEMS AT RESONANCE. 1. Introduction In this article we study the system of ordinary differential equations Electronic Journal of Differential Equations, Vol. 215 (215), No. 148, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu K-DIMENSIONAL NONLOCAL

More information

für Mathematik in den Naturwissenschaften Leipzig

für Mathematik in den Naturwissenschaften Leipzig Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig A short proof of the self-improving regularity of quasiregular mappings. by Xiao Zhong and Daniel Faraco Preprint no.: 106 2002 A

More information

EQUADIFF 1. Rudolf Výborný On a certain extension of the maximum principle. Terms of use:

EQUADIFF 1. Rudolf Výborný On a certain extension of the maximum principle. Terms of use: EQUADIFF 1 Rudolf Výborný On a certain extension of the maximum principle In: (ed.): Differential Equations and Their Applications, Proceedings of the Conference held in Prague in September 1962. Publishing

More information

A Caffarelli-Kohn-Nirenberg type inequality with variable exponent and applications to PDE s

A Caffarelli-Kohn-Nirenberg type inequality with variable exponent and applications to PDE s A Caffarelli-Kohn-Nirenberg type ineuality with variable exponent and applications to PDE s Mihai Mihăilescu a,b Vicenţiu Rădulescu a,c Denisa Stancu-Dumitru a a Department of Mathematics, University of

More information

Higher Integrability of the Gradient of Minimizers of Functionals with Nonstandard Growth Conditions

Higher Integrability of the Gradient of Minimizers of Functionals with Nonstandard Growth Conditions Higher Integrability of the Gradient of Minimizers of Functionals with Nonstandard Growth Conditions NICOLA FUSCO Universitli di Salem0 AND CARL0 SBORDONE Universitli degli Studi, Naples Let us consider

More information

LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR FULLY NONLINEAR ELLIPTIC EQUATIONS

LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR FULLY NONLINEAR ELLIPTIC EQUATIONS Electronic Journal of Differential Equations, Vol. 27 27), No. 2, pp. 3. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu LORENTZ ESTIMATES FOR ASYMPTOTICALLY REGULAR FULLY NONLINEAR

More information

Some Remarks About the Density of Smooth Functions in Weighted Sobolev Spaces

Some Remarks About the Density of Smooth Functions in Weighted Sobolev Spaces Journal of Convex nalysis Volume 1 (1994), No. 2, 135 142 Some Remarks bout the Density of Smooth Functions in Weighted Sobolev Spaces Valeria Chiadò Piat Dipartimento di Matematica, Politecnico di Torino,

More information

Bibliography. Oblique Derivative Problems for Elliptic Equations Downloaded from

Bibliography. Oblique Derivative Problems for Elliptic Equations Downloaded from Bibliography [1] Agmon, S., Douglis, A. and Nirenberg, L. (1959). Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure

More information

Tobias Holck Colding: Publications. 1. T.H. Colding and W.P. Minicozzi II, Dynamics of closed singularities, preprint.

Tobias Holck Colding: Publications. 1. T.H. Colding and W.P. Minicozzi II, Dynamics of closed singularities, preprint. Tobias Holck Colding: Publications 1. T.H. Colding and W.P. Minicozzi II, Dynamics of closed singularities, preprint. 2. T.H. Colding and W.P. Minicozzi II, Analytical properties for degenerate equations,

More information

Symmetry of entire solutions for a class of semilinear elliptic equations

Symmetry of entire solutions for a class of semilinear elliptic equations Symmetry of entire solutions for a class of semilinear elliptic equations Ovidiu Savin Abstract. We discuss a conjecture of De Giorgi concerning the one dimensional symmetry of bounded, monotone in one

More information

Glimpses on functionals with general growth

Glimpses on functionals with general growth Glimpses on functionals with general growth Lars Diening 1 Bianca Stroffolini 2 Anna Verde 2 1 Universität München, Germany 2 Università Federico II, Napoli Minicourse, Mathematical Institute Oxford, October

More information

DIRECTION OF VORTICITY AND A REFINED BLOW-UP CRITERION FOR THE NAVIER-STOKES EQUATIONS WITH FRACTIONAL LAPLACIAN

DIRECTION OF VORTICITY AND A REFINED BLOW-UP CRITERION FOR THE NAVIER-STOKES EQUATIONS WITH FRACTIONAL LAPLACIAN DIRECTION OF VORTICITY AND A REFINED BLOW-UP CRITERION FOR THE NAVIER-STOKES EQUATIONS WITH FRACTIONAL LAPLACIAN KENGO NAKAI Abstract. We give a refined blow-up criterion for solutions of the D Navier-

More information

ANISOTROPIC EQUATIONS: UNIQUENESS AND EXISTENCE RESULTS

ANISOTROPIC EQUATIONS: UNIQUENESS AND EXISTENCE RESULTS ANISOTROPIC EQUATIONS: UNIQUENESS AND EXISTENCE RESULTS STANISLAV ANTONTSEV, MICHEL CHIPOT Abstract. We study uniqueness of weak solutions for elliptic equations of the following type ) xi (a i (x, u)

More information