Regularity for nonlocal equations with local Neumann boundary conditions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911402665443328 |
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| author | Ros-Oton, Xavier Weidner, Marvin |
| author_facet | Ros-Oton, Xavier Weidner, Marvin |
| contents | In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,γ}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v \asymp d^{s-1}$ and are sometimes called large solutions. In this setup we prove optimal regularity results for the quotients $v/d^{s-1}$, depending on the regularity of the domain and on the data of the problem. The results of this article will be important in a forthcoming work on nonlocal free boundary problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_17723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity for nonlocal equations with local Neumann boundary conditions Ros-Oton, Xavier Weidner, Marvin Analysis of PDEs 47G20, 35B65, 31B05, 35R53, 35B44 In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,γ}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v \asymp d^{s-1}$ and are sometimes called large solutions. In this setup we prove optimal regularity results for the quotients $v/d^{s-1}$, depending on the regularity of the domain and on the data of the problem. The results of this article will be important in a forthcoming work on nonlocal free boundary problems. |
| title | Regularity for nonlocal equations with local Neumann boundary conditions |
| topic | Analysis of PDEs 47G20, 35B65, 31B05, 35R53, 35B44 |
| url | https://arxiv.org/abs/2403.17723 |