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Bibliographic Details
Main Author: Lee, Se-Chan
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.16103
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author Lee, Se-Chan
author_facet Lee, Se-Chan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_16103
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nonlocal Harnack inequality in a disconnected region
Lee, Se-Chan
Analysis of PDEs
35B45, 35B65, 35R09
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.
title Nonlocal Harnack inequality in a disconnected region
topic Analysis of PDEs
35B45, 35B65, 35R09
url https://arxiv.org/abs/2508.16103