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

preprint2022arXivOpen access

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $σ_k(D^2u-uI)=C_n^k$ 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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Serrin-type Overdetermined problems in $\mathbb H^n$

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Serrin-type Overdetermined problems in Hn\mathbb H^nHn

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