Quantitative results for fractional overdetermined problems in exterior and annular sets

2022/09/29 by Giulio Ciraolo, Ciraolo, Giulio, Luigi Pollastro +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2209.14679

openalex publication_date 2022/09/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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.

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