On a nonlocal superconductivity problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910052179247104 |
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| author | Araújo, Damião J. Sobral, Aelson |
| author_facet | Araújo, Damião J. Sobral, Aelson |
| contents | This paper investigates degenerate nonlocal free boundary problems arising in the context of superconductivity, extending the nonlocal counterpart to the work of Caffarelli, Salazar, and Shahgholian \cite{CS02, CSS04} in the local setting. In these models, no partial differential equation governs the moving sets where the gradient vanishes, meaning that test functions are only required to have a nonzero gradient. Our main results provide interior gradient Hölder regularity estimates for viscosity solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a nonlocal superconductivity problem Araújo, Damião J. Sobral, Aelson Analysis of PDEs 35B65, 35R11, 35J70, 35R09 This paper investigates degenerate nonlocal free boundary problems arising in the context of superconductivity, extending the nonlocal counterpart to the work of Caffarelli, Salazar, and Shahgholian \cite{CS02, CSS04} in the local setting. In these models, no partial differential equation governs the moving sets where the gradient vanishes, meaning that test functions are only required to have a nonzero gradient. Our main results provide interior gradient Hölder regularity estimates for viscosity solutions. |
| title | On a nonlocal superconductivity problem |
| topic | Analysis of PDEs 35B65, 35R11, 35J70, 35R09 |
| url | https://arxiv.org/abs/2508.20841 |