Quantitative results for fractional overdetermined problems in exterior and annular sets
Analysis of PDEs
2023-01-26 v2
Abstract
We consider overdetermined problems related to the fractional capacity. In particular we study -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.
Keywords
Cite
@article{arxiv.2209.14679,
title = {Quantitative results for fractional overdetermined problems in exterior and annular sets},
author = {Giulio Ciraolo and Luigi Pollastro},
journal= {arXiv preprint arXiv:2209.14679},
year = {2023}
}