Optimal boundary regularity for mixed local and nonlocal equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918239472189440 |
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| author | Abatangelo, Nicola Affili, Elisa Cozzi, Matteo |
| author_facet | Abatangelo, Nicola Affili, Elisa Cozzi, Matteo |
| contents | We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian.
Our approach makes use of weighted Hölder spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument.
We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal boundary regularity for mixed local and nonlocal equations Abatangelo, Nicola Affili, Elisa Cozzi, Matteo Analysis of PDEs We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach makes use of weighted Hölder spaces as well as regularity estimates for the Laplacian in this context and a fixed-point argument. We show the optimality of the obtained estimates by means of a counterexample that we have striven to keep as explicit as possible. |
| title | Optimal boundary regularity for mixed local and nonlocal equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.13711 |