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arXiv · 2608.07315

Hölder regularity and Harnack inequality for the logarithmic Laplacian

Anup Biswas·Subhajit Roy·Aniket Sen·Lovelesh Sharma
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Abstract

In this article, we establish Schauder-type estimates for the logarithmic Laplacian. We show that for a $κ$-Hölder inhomogeneous term, the solution is also $κ$-Hölder in the interior. In fact, the interior regularity slightly exceeds $κ$-Hölder smoothness up to a logarithmic correction. Additionally, we prove a Harnack inequality for non-negative solutions.

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Anup Biswas, Subhajit Roy, Aniket Sen, Lovelesh Sharma. 2026-08-07. Hölder regularity and Harnack inequality for the logarithmic Laplacian. https://arxiv.org/abs/2608.07315

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