A partially overdetermined problem in a half ball
Analysis of PDEs
2019-08-08 v3
Abstract
In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap intersecting orthogonally. As an application, we show a stationary point for a partially torsional rigidity under a volume constraint must be a spherical cap.
Cite
@article{arxiv.1807.01507,
title = {A partially overdetermined problem in a half ball},
author = {Jinyu Guo and Chao Xia},
journal= {arXiv preprint arXiv:1807.01507},
year = {2019}
}
Comments
Final version, to appear in Calc. Var. PDEs