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

Bo Wang; Zhizhang Wang

doi:10.1016/j.aim.2025.110737

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

Bo Wang^*
, Zhizhang Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	110737
Journal	Advances in Mathematics
Volume	485
DOIs	https://doi.org/10.1016/j.aim.2025.110737
Publication status	Published - Feb 2026
Externally published	Yes

Keywords

Exterior domain
Hessian equations
Legendre transform
Over-determined problem
Rigidity

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10.1016/j.aim.2025.110737

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title = "A Serrin-type over-determined problem for Hessian equations in the exterior domain",

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.",

keywords = "Exterior domain, Hessian equations, Legendre transform, Over-determined problem, Rigidity",

author = "Bo Wang and Zhizhang Wang",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2026",

month = feb,

doi = "10.1016/j.aim.2025.110737",

language = "English",

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T1 - A Serrin-type over-determined problem for Hessian equations in the exterior domain

AU - Wang, Bo

AU - Wang, Zhizhang

PY - 2026/2

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N2 - 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.

AB - 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.

KW - Exterior domain

KW - Hessian equations

KW - Legendre transform

KW - Over-determined problem

KW - Rigidity

UR - https://www.scopus.com/pages/publications/105024910533

U2 - 10.1016/j.aim.2025.110737

DO - 10.1016/j.aim.2025.110737

M3 - Article

AN - SCOPUS:105024910533

SN - 0001-8708

VL - 485

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 110737

ER -

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

Abstract

Keywords

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