English

Radial symmetry and partially overdetermined problems in a convex cone

Differential Geometry 2020-09-02 v1 Analysis of PDEs

Abstract

We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function PP and integral identities. In dimension 22, we prove Serrin-type results for partially overdetermined problems outside a convex cone. Furthermore, we obtain a Rellich identity for an eigenvalue problem with mixed boundary conditions in a cone.

Keywords

Cite

@article{arxiv.2009.00280,
  title  = {Radial symmetry and partially overdetermined problems in a convex cone},
  author = {Jihye Lee and Keomkyo Seo},
  journal= {arXiv preprint arXiv:2009.00280},
  year   = {2020}
}