Overdetermined Boundary Value Problems in $\mathbb{S}^n$

Authors

  • Guohuan Qiu Department of Mathematics and Statistics, McGill University, Montreal, H3A 0B9, Canada
  • Chao Xia School of Mathematical Sciences, Xiamen University, Xiamen 361005, P.R. China

DOI:

https://doi.org/10.4208/jms.v50n2.17.03

Keywords:

Overdetermined problems, Schiffer's problem, $P$-function.

Abstract

In this paper we use the maximum principle and the Hopf lemma to prove symmetry results to some overdetermined boundary value problems for domains in the hemisphere or star-shaped domains in $S^n$. Our method is based on finding suitable $P$-functions as Weinberger ([26]).

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Published

2017-06-02

Issue

Vol. 50 No. 2 (2017)

Section

Articles