Xujia Wang, Ph. D.
▎Professor of Mathematics
▎Partial Differential Equations Group
◢ Website：
◢ Email：wangxujia@westlake.edu.cn
Biography
Xu-Jia Wang was studying in the Department of Mathematics, Zhejiang University from 9/1979 until he received his Ph.D. in 1990. He was then a Lecturer and Associate Professor at Zhejiang Univ. He accepted a Research Fellow position at the Australian National University in Sept 1995, and was promoted to Professor in 2005. He was awarded the Morningside Gold Medal in Mathematics in 2007, was elected as a Fellow of the Australian Academy of Sciences in 2009 and was awarded the Laureate Fellowship in 2013. In Sept 2024, he joined Westlake University.
Research
Xu-Jia Wang is mainly engaged in the theory of nonlinear elliptic and parabolic equations and their applications in geometry and physics. The main research outputs include (mostly with collaborators): established the potential theory of Hessian equations, proved the regularity of free boundaries in the Monge-Ampere equation, and obtained the optimal regularity for the boundary value problems of the Monge-Ampere equation. Resolved Chern’s conjecture on the affine Bernstein problem, made a breakthrough on the singularity profiles of the mean curvature flow. Obtained the existence of solutions to the optimal transport problem raised by Monge in 1781 and established the regularity for the optimal transport problem with general cost functions and therefore answered a question raised by Villani.
Representative Publications
1) Shibing Chen, Jiakun Liu, Xu-Jia Wang, Global regularity for the Monge-Ampère equation with natural boundary condition, Ann. Math., 194 (2021), 745-793.
2) Xu-Jia Wang, Counterexample to the convexity of level sets of solutions to the mean curvature equation, J. Euro. Math. Soc., 16 (2014), 1173-1182.
3) Xu-Jia Wang, Convex solutions to the mean curvature flow, Ann. Math., 173 (2011), 1185-1239.
4) Neil Trudinger, Xu-Jia Wang, Boundary regularity for the Monge-Ampere and affine maximal surface equations, Ann. Math., 167 (2008), 993-1028.
5) Xu-Jia Wang, Schauder estimates for elliptic and parabolic equations, Chinese Ann. Math., 27 (2006), 637-642.
6) Xi-Nan Ma, Neil Trudinger, Xu-Jia Wang, Regularity of potential functions of the optimal transportation problem, Arch. Rat. Mech. Anal., 177 (2005), 151-183.
7) Neil Trudinger, Xu-Jia Wang, The Bernstein problem for affine maximal hypersurfaces, Invent. Math., 140 (2000), 399-422.
8) Neil Trudinger, Xu-Jia Wang, Hessian measures II, Ann. Math., 150 (1999) 579-604.
9) Xu-Jia Wang, A class of fully nonlinear elliptic equations and related functional, Indiana Univ. Math. J., 43(1994), 25-54.
10) Xu-Jia Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Equa., 93(1991), 283-310.
Contact Information
Email：wangxujia@westlake.edu.cn
