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

Published 12 Jan 2022 in math.AP | (2201.04323v1)

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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