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arXiv · 2201.04323

Serrin-type Overdetermined problems in $\mathbb H^n$

Zhenghuan Gao·Xiaohan Jia·Jin Yan
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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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Zhenghuan Gao, Xiaohan Jia, Jin Yan. 2022-01-12. Serrin-type Overdetermined problems in $\mathbb H^n$. https://arxiv.org/abs/2201.04323

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