Global Calderón-Zygmund theory for fractional Laplacian type equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929558046900224 |
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| author | Byun, Sun-Sig Kim, Kyeong Bae Kumar, Deepak |
| author_facet | Byun, Sun-Sig Kim, Kyeong Bae Kumar, Deepak |
| contents | We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund type estimates of $u/d^s$ depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the Hölder continuity, where $u$ is a weak solution to such a nonlocal problem and $d$ is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of $u/d^s$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19243 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Calderón-Zygmund theory for fractional Laplacian type equations Byun, Sun-Sig Kim, Kyeong Bae Kumar, Deepak Analysis of PDEs We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund type estimates of $u/d^s$ depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the Hölder continuity, where $u$ is a weak solution to such a nonlocal problem and $d$ is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of $u/d^s$. |
| title | Global Calderón-Zygmund theory for fractional Laplacian type equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.19243 |