Semiconvexity estimates for nonlinear integro-differential equations
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Oviedo (UNIOVI) |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:dnet:ubarcelona__::350535579a71761fd9781a261858a995 |
| Acceso en línea: | https://hdl.handle.net/2445/229554 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria d&apos operadors Equacions en derivades parcials Teoria del potencial (Matemàtica) Processos de Markov Operator theory Partial differential equations Potential theory (Mathematics) Markov processes |
| Sumario: | In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré-Dipierro-Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators. |
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