$\mathbb H^n$中的serrin型超定问题

Pub Date : 2022-01-12 DOI:10.4208/jpde.v36.n1.7

Zhenghuan Gao, Xiaohan Jia, Jingquan Yan

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引用次数: 1

摘要

本文证明了双曲空间中方程σk(d2 u−uI) = cn的超定问题解的对称性。我们的方法是基于建立RellichPohozaev类型恒等式和使用P函数。我们的结果推广了欧几里德空间中Hessian方程的过定问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σk(D 2 u − uI) = C n in hyperbolic space. Our approach is based on establishing a RellichPohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.

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