Quantitative results for fractional overdetermined problems in exterior and annular sets

Giulio Ciraolo; Luigi Pollastro

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arXiv · 2209.14679

Quantitative results for fractional overdetermined problems in exterior and annular sets

Giulio Ciraolo·Luigi Pollastro

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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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Giulio Ciraolo, Luigi Pollastro. 2022-09-29. Quantitative results for fractional overdetermined problems in exterior and annular sets. https://arxiv.org/abs/2209.14679

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