JIUYI ZHU 313 Krieger Hall Cell: 313-404-0997 Department of Mathematics Phone: 410-516-0156 (Office) Johns Hopkins University Fax: 410-516-5549 3400 N. Charles Street Email: jzhu43@math.jhu.edu Baltimore, MD 21218 URL: http://www.math.jhu.edu/ jzhu43 Education Ph.D. in Mathematics, June 2013 Wayne State University, Detroit, USA Advisor: Prof. Guozhen Lu Master of Arts in Mathematical Statistics, September 2012 Wayne State University, Detroit, USA Master of Science in Applied Mathematics, June 2008 Hunan Normal University, Changsha, China Bachelor of Science in Applied Mathematics, June 2005 Hunan University, Changsha, China Work Experience J.J. Sylvester Assistant Professor, Johns Hopkins University, Fall 2013 Present Research Interests Partial Differential Equations and Their Applications: Qualitative and quantitative properties of solutions, Geometric inequalities, Reaction-Diffusion equations, Sub-elliptic equations, Inverse problems, Fully nonlinear partial differential equations, etc. Harmonic Analysis: Unique continuation problems, Carleman estimates, Microlocal analysis, Dispersive equations, Global estimates for eigenfunctions, etc. Geometric Analysis: Geometric properties of eigenfunctions Grants 2015-2018 2014 2016 NSF Grant: DMS-1500468 AMS-Simons Travel Grant 1
Publications 1. A lower bound for nodal sets of Steklov eigenfunctions, to appear in Mathematical Research Letters (with X. Wang). 2. Doubling property and vanishing order of Steklov eigenfunctions, to appear in Communications in Partial differential equations 3. Quantitative uniqueness of elliptic equations, to appear in American Journal of Mathematics 4. Maximum principles and symmetry results of viscosity solutions for fully nonlinear equations, Journal of Differential Equations 258(2015), 2054-2079 (with G. Lu). 5. The improved Moser-Trudinger inequality with L p norm in n dimensions, Advanced Nonlinear Studies 14 (2014), no. 2, 273-293. 6. Liouville-type theorems for fully nonlinear elliptic equations in half spaces, Advanced Nonlinear Studies 13 (2013), 979-1001 (G. Lu). 7. Liouville-type theorems and decay estimates for solutions to higher order elliptic equations, Annales de l Institut Henri Poincaré(C) Analyse Non Linéaire 29(2012), no. 5, 653-665 (with G. Lu and P. Wang). 8. Hardy-Littlewood-Sobolev and Stein-Weiss inequalities and integral systems on the Heisenberg group, Nonlinear Analysis: Theory, Methods & Applications 75(2012), no. 11, 4296-4314 (with X. Han and G. Lu). 9. Characterization of balls in terms of Bessel-potential integral equation, Journal of Differential Equations 252(2012), no. 2, 1589-1602 (with X. Han and G. Lu). 10. An overdetermined problem in Riesz-potential and fractional Laplacian, Nonlinear Analysis: Theory, Methods & Applications 75(2012), no. 6, 3036-3048 (with G. Lu). 11. The axial symmetry and regularity of solutions to an integral equation in a half space, Pacific Journal of Mathematics 253(2011), no. 2, 455-473 (with G. Lu). 12. A priori estimates, existence and nonexistence of positive solutions of generalized mean curvature equations, Nonlinear Analysis: Theory, Methods & Applications 74(2011), no. 18, 7126-7136 (with Q. Dai and Y. Gu). 13. Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality, Calculus of Variations and Partial Differential Equations 42(2011), no. 3-4, 563-577 (with G. Lu). 14. Radial symmetry and regularity of solution for poly-harmonic Dirichlet problems, Journal of Mathematical Analysis and Applications 377(2011), no. 2, 744-753 (with W. Chen). Preprints 15. Lower bounds for interior nodal sets of Steklov eigenfunctions, arxiv:1503.01091 (with Chris Sogge and X. Wang). 2
16. Indefinite fractional elliptic problems and Liouville theorems, arxiv:1404.1640, submitted (with W. Chen). Professional Service Co-organizer, AMS 2015 Spring Northeastern Sectional Meeting, special session Qualitative behavior of solutions of partial differential equations, (with J. Shi), Georgetown University, March 7-8, 2015 Analysis and PDE Seminar Organizer, Johns Hopkins, 2013-2014 Refereed articles for Nonlinear Analysis: Theory, Methods & Applications, Acta Mathematics Sinica, Discrete and Continuous Dynamical Systems Series A, Communications on Pure and Applied Analysis, Applied Mathematics and Computation Reviewer of Mathematical Reviews Academic Activities Selected Talks May 22-25, 2015, Wuhan Harmonic analysis conference, Central China Normal University March 14-15, 2015, AMS Central Spring Sectional Meeting, Michigan State University March 7-8, 2015, AMS Spring Northeastern Sectional Meeting, Georgetown University February 02, 2015, Analysis and PDEs seminar, Johns Hopkins University November 21, 2014, Geometry and Geometric analysis seminar, Princeton University May 12-16, 2014, Kinetics, non-standard diffusions and stochastics: emerging challenges in the sciences, University of Texas at Austin March 28, 2014, Colloquium, The College of William & Mary March 13-15, 2014, International Workshop Advances in Nonlinear Analysis, University of Pittsburgh March 8-9, 2014, The 4th Ohio River Analysis Meeting, University of Kentucky November 25, 2013, Differential equations seminar, University of Maryland Baltimore County October 30 and November 6, 2013, Hopkins Analysis Workshop, Johns Hopkins University February 13, 2013, PDEs seminar, Wayne State University January 11, 2013, 2013 Joint Mathematics Meetings, San Diego, CA September 24-28, 2012, Poster Presentation, Dynamical Systems in Studies of Partial Differential Equations, Institute for Mathematics and its Applications May 20-23, 2012, The 5th Symposium on Analysis and PDEs, Purdue University March 6, 2012, The 3rd Annual Graduate Exhibition, Wayne State University October 5 and October 12, 2011, PDEs seminar, Wayne State University 3
May 12-14, 2011, International Conference: Recent Development on L -Variational Problems and Associated Nonlinear Partial Differential Equations, University of Kentucky March 19-20, 2011, 67th Midwest Partial Differential Equations Seminar, University of Illinois at Urbana-Champaign January 19 and January 26, 2011, PDEs seminar, Wayne State University Conferences and Workshops Attended April 17-19, 2015, The Eighteenth Rivière-Fabes symposium on Analysis and PDE, University of Minnesota June 9-20, 2014, Thematic Program on Nonlinear PDEs in Geometry and Physics, University of Notre Dame May 7-18, 2012, Concentration month on Nonlinear Elliptic PDEs, University of Chicago April 20-22, 2012, The Fifteenth Rivière-Fabes symposium on Analysis and PDE, University of Minnesota November 4-6, 2011, 68th Midwest Partial Differential Equations Seminar, University of Notre-Dame January 29-30, 2011, Ohio River Analysis Meeting, University of Cincinnati July 12-August 6, 2010, The Summer School in Partial Differential Equations, East China Normal University, China July 6-9, 2010, The Seventh East China Partial Differential Equations Conference, Huazhong Normal University, China November 14-15, 2009, Workshop on Fourier and Harmonic Analysis, Wayne State University Awards and Honors 2012-1013, Max Coral Award for outstanding achievement in the Ph.D. Program, Wayne State University 2012-1013, Outstanding Graduate Research Award, Wayne State University 2011 2012, Maurice J. Zelonka Endowed Mathematics Scholarship, Wayne State University 2010 2011, Maurice J. Zelonka Endowed Mathematics Scholarship, Wayne State University 2010 2013, Graduate Student Professional Travel Awards, Wayne State University Teaching September 2013 Present, Department of Mathematics, Johns Hopkins University Differential Equations with Applications (MAT 302), Lecture course with 7 sections, Spring 2015 Fourier Analysis (MAT 443), Fall 2014 4
Honors Analysis II (MAT 416), Spring 2014 Partial Differential Equations for Applications (MAT 417), Spring 2014 Fourier Analysis (MAT 443), Fall 2013 September 2008 August 2012, Graduate Teaching Assistant, Department of Mathematics, Wayne State University Served as the sole instructor with full responsibility in the following classes: Probability and Statistics for Teachers (MAT 6150), Spring/Summer 2012 Probability and Statistics (MAT 2210), Spring/Summer 2012 Calculus I (MAT 2010), Spring/Summer 2011 Pre-calculus (MAT 1800), Fall 2011 and Winter 2012 College Algebra for the Social and Management Sciences (MAT 1500), Spring/Summer 2011 Algebra with Trigonometry (MAT 1050), Winter 2009, Fall 2009, Winter 2010, and Winter 2011 Beginning Algebra (MAT 0993), Fall 2010 Computer Skills C, L A TEX, Matlab, and Mathematica 5