Nonlocal Harnack inequality in a disconnected region
Analysis of PDEs
2025-08-25 v1
Abstract
We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal phenomenon with no local analogue. We provide two different approaches: one based on the localized maximum principle and another on the Poisson kernel estimates.
Cite
@article{arxiv.2508.16103,
title = {Nonlocal Harnack inequality in a disconnected region},
author = {Se-Chan Lee},
journal= {arXiv preprint arXiv:2508.16103},
year = {2025}
}
Comments
15 pages