A Serrin-type over-determined problem for Hessian equations in the exterior domain

Published 16 Dec 2024 in math.AP | (2412.11841v1)

Abstract: In this paper, we consider the Hessian equations in some exterior domain with prescribed asymptotic behavior at infinity and Dirichlet-Neumann conditions on its interior boundary. We obtain that there exists a unique bounded domain such that the over-determined problem admits a unique strictly convex solution.

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