一类多扰动Serrin问题的稳定性
Stability of a class of a Serrin's problem with multiple perturbations
李雨薇 1马飞遥 1陈传强1
作者信息
- 1. 宁波大学数学与统计学院,浙江 宁波 315211
- 折叠
摘要
本文研究了一个具有未知子域及边界条件有扰动的Serrin超定问题的稳定性.根据度量域与球的偏差,从而建立了一个定量的稳定性估计.利用Rellich-Pohozaev-type型积分等式,证明当未知子域的勒贝格测度小且边界上的法向导数趋于一个常数时,域在几何上接近于一个球.
Abstract
In this paper,we investigate the stability of a Serrin-type overdetermined problem with perturbations in the unknown subdomain and boundary conditions.A quantitative stability estimate is established by measuring the deviation between the domain and a sphere.We prove that when the subdomain has a small Lebesgue measure and the outward normal derivative on the boundary approaches a constant,the domain is geometrically close to a sphere.The proof is based on a Rellich-Pohozaev-type integral identity.
关键词
超定问题/积分等式/稳定性分析/定量估计Key words
overdetermined problem/integral identity/stability analysis/quantitative estimates引用本文复制引用
出版年
2024
NETL
NSTL
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