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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.14639 |
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Table of Contents:
- For $0<s<1$, we consider the nonlocal equation $(-Δ)^s u = f$ over a Reifenberg flat domain $Ω$ with $f \in C({\overlineΩ})$ and null Dirichlet exterior condition. Given $α\in (0,s)$, we prove that weak solutions are $α$-Hölder 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.