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 and integral identities. In dimension , 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.
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}
}