Parabolic Boundary Harnack Inequalities with Right-Hand Side
We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by blow-up techniques, allowing, for the first time, a non-zero right-hand side. Our method allows us to treat solutions to equations driven by non-divergence form operators with bounded measurable coefficients, a...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:dnet:ubarcelona__::5efbc0f681c4cfbf86526fa0ea08a949 |
| Acceso en línea: | https://hdl.handle.net/2445/228884 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria hiperbòlica Equacions en derivades parcials Equacions diferencials parcials estocàstiques Hyperbolic geometry Partial differential equations Stochastic partial differential equations |
| Sumario: | We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by blow-up techniques, allowing, for the first time, a non-zero right-hand side. Our method allows us to treat solutions to equations driven by non-divergence form operators with bounded measurable coefficients, and a right-hand side $f \in L^q$ for $q>n+2$. In the case of the heat equation, we also show the optimal $C^{1-\varepsilon}$ regularity of the quotient. As a corollary, we obtain a new way to prove that flat Lipschitz free boundaries are $C^{1, \alpha}$ in the parabolic obstacle problem and in the parabolic Signorini problem. |
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