English

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 \ssn1\ss^{n-1} orthogonally. As an application, we show a stationary point for a partially torsional rigidity under a volume constraint must be a spherical cap.

Keywords

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

R2 v1 2026-06-23T02:50:24.154Z