Boundary Hölder regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913664718602240 |
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| author | Prade, Adriano |
| author_facet | Prade, Adriano |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Hölder regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle Prade, Adriano Analysis of PDEs 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. |
| title | Boundary Hölder regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.14639 |