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Serrin-Type Overdetermined Problem in $\mathbb H^n$
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@Article{JPDE-36-102,
author = {Gao , ZhenghuanJia , Xiaohan and Yan , Jin},
title = {Serrin-Type Overdetermined Problem in $\mathbb H^n$},
journal = {Journal of Partial Differential Equations},
year = {2022},
volume = {36},
number = {1},
pages = {102--118},
abstract = {
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.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.7}, url = {http://global-sci.org/intro/article_detail/jpde/21296.html} }
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 -
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.
Zhenghuan Gao, Xiaohan Jia & Jin Yan. (2022). Serrin-Type Overdetermined Problem in $\mathbb H^n$.
Journal of Partial Differential Equations. 36 (1).
102-118.
doi:10.4208/jpde.v36.n1.7
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