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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02448 |
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| _version_ | 1866929278778605568 |
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| author | Iannizzotto, Antonio Mosconi, Sunra |
| author_facet | Iannizzotto, Antonio Mosconi, Sunra |
| contents | We study the boundary weighted regularity of weak solutions $u$ to a $s$-fractional $p$-Laplacian equation in a bounded smooth domain $Ω$ with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case $p\in(1,2)$ and with $s\in(0,1)$. We prove that $u/{\rm d}_Ω^s$ has a $α$-Hölder continuous extension to the closure of $Ω$, ${\rm d}_Ω(x)$ meaning the distance of $x$ from the complement of $Ω$. This result corresponds to that of ref. [28] for the degenerate case $p\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fine boundary regularity for the singular fractional p-Laplacian Iannizzotto, Antonio Mosconi, Sunra Analysis of PDEs 35D10, 35R11, 47G20 We study the boundary weighted regularity of weak solutions $u$ to a $s$-fractional $p$-Laplacian equation in a bounded smooth domain $Ω$ with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case $p\in(1,2)$ and with $s\in(0,1)$. We prove that $u/{\rm d}_Ω^s$ has a $α$-Hölder continuous extension to the closure of $Ω$, ${\rm d}_Ω(x)$ meaning the distance of $x$ from the complement of $Ω$. This result corresponds to that of ref. [28] for the degenerate case $p\ge 2$. |
| title | Fine boundary regularity for the singular fractional p-Laplacian |
| topic | Analysis of PDEs 35D10, 35R11, 47G20 |
| url | https://arxiv.org/abs/2402.02448 |