English

Serrin-type Overdetermined problems in $\mathbb H^n$

Analysis of PDEs 2022-01-13 v1

Abstract

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σk(D2uuI)=Cnk\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.

Keywords

Cite

@article{arxiv.2201.04323,
  title  = {Serrin-type Overdetermined problems in $\mathbb H^n$},
  author = {Zhenghuan Gao and Xiaohan Jia and Jin Yan},
  journal= {arXiv preprint arXiv:2201.04323},
  year   = {2022}
}
R2 v1 2026-06-24T08:47:20.793Z