Singularities of solutions of nonlocal nonlinear equations
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915375105441792 |
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| author | Kim, Minhyun Lee, Se-Chan |
| author_facet | Kim, Minhyun Lee, Se-Chan |
| contents | We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularities of solutions of nonlocal nonlinear equations Kim, Minhyun Lee, Se-Chan Analysis of PDEs 35A21, 35B65, 35R09 We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution. |
| title | Singularities of solutions of nonlocal nonlinear equations |
| topic | Analysis of PDEs 35A21, 35B65, 35R09 |
| url | https://arxiv.org/abs/2410.13292 |