TY - JOUR
T1 - Serrin-Type Overdetermined Problem in $\mathbb H^n$
AU - Gao , Zhenghuan
AU - Jia , Xiaohan
AU - Yan , Jin
JO - Journal of Partial Differential Equations
VL - 1
SP - 102
EP - 118
PY - 2022
DA - 2022/12
SN - 36
DO - http://doi.org/10.4208/jpde.v36.n1.7
UR - https://global-sci.org/intro/article_detail/jpde/21296.html
KW - Overdetermined problems
KW - hyperbolic space
KW - P functions
KW - Rellich-Pohozaev identity.
AB - <p style="text-align: justify;">In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $\sigma_k(D^2u-uI)=C_n^k$ in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a $P$ function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.</p>