English

A Serrin-type over-determined problem for Hessian equations in the exterior domain

Analysis of PDEs 2024-12-17 v1

Abstract

In this paper, we consider the Hessian equations in some exterior domain with prescribed asymptotic behavior at infinity and Dirichlet-Neumann conditions on its interior boundary. We obtain that there exists a unique bounded domain such that the over-determined problem admits a unique strictly convex solution.

Keywords

Cite

@article{arxiv.2412.11841,
  title  = {A Serrin-type over-determined problem for Hessian equations in the exterior domain},
  author = {Bo Wang and Zhizhang Wang},
  journal= {arXiv preprint arXiv:2412.11841},
  year   = {2024}
}