Liouville theorem for singular solutions to nonlocal equations

Minhyun Kim; Se-Chan Lee

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arXiv · 2507.09587

Liouville theorem for singular solutions to nonlocal equations

Minhyun Kim·Se-Chan Lee

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Abstract

We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the singular point. In addition, we prove Liouville theorems for singular solutions. To this end, we construct fundamental solutions for nonlocal linear operators and establish a localized comparison principle.

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Minhyun Kim, Se-Chan Lee. 2025-07-13. Liouville theorem for singular solutions to nonlocal equations. https://arxiv.org/abs/2507.09587

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