@Article{JMS-50-165, author = {Qiu , Guohuan and Xia , Chao}, title = {Overdetermined Boundary Value Problems in $\mathbb{S}^n$}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {2}, pages = {165--173}, 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]).

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n2.17.03}, url = {http://global-sci.org/intro/article_detail/jms/10007.html} }