Quantitative results for fractional overdetermined problems in exterior and annular sets

被引：0
|
作者：
Ciraolo, Giulio [1 ]
Pollastro, Luigi [1 ]
机构：
[1] Univ Milan, Dipartimento Matemat Federigo Enriques, Via Cesare Saldini 50, I-20133 Milan, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 524卷 / 01期
关键词：
Fractional Laplacian; Overdetermined problems; Exterior problems; Annular domains; Quantitative stability; LEVEL SURFACE PARALLEL; LAPLACIAN; SYMMETRY;
D O I：
10.1016/j.jmaa.2023.127070
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider overdetermined problems related to the fractional capacity. In particular we study s-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first classify the solutions of the overdetermined problems, by proving that the domain and the solution itself are radially symmetric. Then we prove a quantitative stability counterpart of the symmetry results: we assume that the overdetermined condition is slightly perturbed and we measure, in a quantitative way, how much the domain is close to a symmetric set. (c) 2023 Elsevier Inc. All rights reserved.
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页数：18
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