Serrin-Type Overdetermined Problem in $\mathbb H^n$

Authors

  • Zhenghuan Gao Department of Mathematics, Shanghai University, Shanghai 200444, China.
  • Xiaohan Jia School of Mathematical Sciences, Xiamen University, Xiamen 361005, China.
  • Jin Yan School of Mathematical Sciences, University of Science and Technology of China, Hefei 230025, China.

DOI:

https://doi.org/10.4208/jpde.v36.n1.7

Keywords:

Overdetermined problems;hyperbolic space;P functions;Rellich-Pohozaev identity.

Abstract

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $\sigma_k(D^2u-uI)=C_n^k$ in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a $P$ function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.

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Published

2023-06-16

Issue

Vol. 36 No. 1 (2023)

Section

Articles