Nonlinear nonlocal equations in Reifenberg flat domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916905051226112 |
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| author | Byun, Sun-Sig Kim, Kyeongbae Song, Kyeong |
| author_facet | Byun, Sun-Sig Kim, Kyeongbae Song, Kyeong |
| contents | We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish several fine boundary regularity results for solutions, and their gradient, near the boundary. To the best of our knowledge, each of our results is new even in the linear case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear nonlocal equations in Reifenberg flat domains Byun, Sun-Sig Kim, Kyeongbae Song, Kyeong Analysis of PDEs We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish several fine boundary regularity results for solutions, and their gradient, near the boundary. To the best of our knowledge, each of our results is new even in the linear case. |
| title | Nonlinear nonlocal equations in Reifenberg flat domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.12595 |