TY - JOUR
T1 - Overdetermined Boundary Value Problems in $\mathbb{S}^n$
AU - Qiu , Guohuan
AU - Xia , Chao
JO - Journal of Mathematical Study
VL - 2
SP - 165
EP - 173
PY - 2017
DA - 2017/06
SN - 50
DO - http://doi.org/10.4208/jms.v50n2.17.03
UR - https://global-sci.org/intro/article_detail/jms/10007.html
KW - Overdetermined problems, Schiffer's problem, $P$-function.
AB - <p style="text-align: justify;">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]).</p>