@article{Lee2025, 
author = {Se-Chan Lee},
title = {Nonlocal Harnack inequality in a disconnected region},
year = {2025},
journal = {Mathematics in Engineering},
volume = {7},
number = {6},
pages = {678-694},
keywords = {Harnack inequality, nonlocal equation, disconnected region, Poisson kernel, maximum principle},
url = {https://www.sciopen.com/article/10.3934/mine.2025028},
doi = {10.3934/mine.2025028},
abstract = {We establish a Harnack inequality for weak solutions of nonlocal nonlinear equations in a disconnected region. The inequality compares the value of a solution on one connected component with that on another, capturing a purely nonlocal phenomenon with no local analogue. We provide three different approaches based on a new weak Harnack inequality, the Poisson formula and the localized maximum principle.}
}