Existence and regularity in the fully nonlinear one-phase free boundary problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915113359900672 |
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| author | Carducci, Matteo Velichkov, Bozhidar |
| author_facet | Carducci, Matteo Velichkov, Bozhidar |
| contents | We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existence of viscosity solutions via the Perron's method and we prove $C^{2,α}$ regularity of flat free boundaries via a quadratic improvement of flatness. Finally, we obtain the higher regularity of the free boundary via an hodograph transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and regularity in the fully nonlinear one-phase free boundary problem Carducci, Matteo Velichkov, Bozhidar Analysis of PDEs We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existence of viscosity solutions via the Perron's method and we prove $C^{2,α}$ regularity of flat free boundaries via a quadratic improvement of flatness. Finally, we obtain the higher regularity of the free boundary via an hodograph transform. |
| title | Existence and regularity in the fully nonlinear one-phase free boundary problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.12101 |