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arXiv · 2508.16103

Nonlocal Harnack inequality in a disconnected region

Se-Chan Lee
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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.

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Se-Chan Lee. 2025-08-22. Nonlocal Harnack inequality in a disconnected region. https://arxiv.org/abs/2508.16103

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