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arXiv · 2501.14639

Boundary H\"older regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle

Adriano Prade
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Abstract

For $0<s<1$, we consider the nonlocal equation $(-\Delta)^s u = f$ over a Reifenberg flat domain $\Omega$ with $f \in C({\overline{\Omega}})$ and null Dirichlet exterior condition. Given $\alpha \in (0,s)$, we prove that weak solutions are $\alpha$-H\"older continuous up to the boundary when the flatness parameter is small enough. The main ingredients of the proof are an iterative argument and a nonlocal version of the ABP maximum principle.

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Adriano Prade. 2025-01-24. Boundary H\"older regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle. https://arxiv.org/abs/2501.14639

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