On overdetermind problems for a general class of nonlocal operators
Analysis of PDEs
2025-06-23 v2
Abstract
We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider these problems in bounded domains, exterior domains, and in annular domains and we show that under suitable conditions, the domains and solutions are both radially symmetric. Our method uses both analytic and probabilistic tools.
Cite
@article{arxiv.1904.01917,
title = {On overdetermind problems for a general class of nonlocal operators},
author = {Anup Biswas and Sven Jarohs},
journal= {arXiv preprint arXiv:1904.01917},
year = {2025}
}
Comments
Added a missing assumption in Theorems 2.1, 2.2, and 2.3, which is used in the proof of Lemma 3.2