Year: 2023
Author: Xiaohan Jia, Zhenghuan Gao, Jin Yan, Xiaohan Jia, Jin Yan
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n1.7
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 102–118
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Overdetermined problems