Serrin-Type Overdetermined Problem in $\mathbb H^n$

Serrin-Type Overdetermined Problem in $\mathbb H^n$

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

Author Details

Xiaohan Jia

Zhenghuan Gao

Jin Yan

Xiaohan Jia

Jin Yan