Fully nonlinear parabolic fixed transmission problems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912501163098112 |
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| author | Jesus, David Soria-Carro, María |
| author_facet | Jesus, David Soria-Carro, María |
| contents | We consider transmission problems for parabolic equations governed by distinct fully nonlinear operators on each side of a time-dependent interface. We prove that if the interface is $C^{1,α}$, in the parabolic sense, then viscosity solutions are piecewise $C^{1,α}$ up to the interface. As byproducts, we obtain a new ABP-Krylov-Tso estimate, and establish existence, uniqueness, a comparison principle, and regularity results for the flat interface problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fully nonlinear parabolic fixed transmission problems Jesus, David Soria-Carro, María Analysis of PDEs 35B65, 35J60 (Primary) 35K10, 35D40 (Secondary) We consider transmission problems for parabolic equations governed by distinct fully nonlinear operators on each side of a time-dependent interface. We prove that if the interface is $C^{1,α}$, in the parabolic sense, then viscosity solutions are piecewise $C^{1,α}$ up to the interface. As byproducts, we obtain a new ABP-Krylov-Tso estimate, and establish existence, uniqueness, a comparison principle, and regularity results for the flat interface problem. |
| title | Fully nonlinear parabolic fixed transmission problems |
| topic | Analysis of PDEs 35B65, 35J60 (Primary) 35K10, 35D40 (Secondary) |
| url | https://arxiv.org/abs/2507.19277 |