Semiconvexity estimates for nonlinear integro-differential equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912101005524992 |
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| author | Ros-Oton, Xavier Torres-Latorre, Clara Weidner, Marvin |
| author_facet | Ros-Oton, Xavier Torres-Latorre, Clara Weidner, Marvin |
| contents | 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 [CDV22]. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16751 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semiconvexity estimates for nonlinear integro-differential equations Ros-Oton, Xavier Torres-Latorre, Clara Weidner, Marvin Analysis of PDEs 47G20, 35B65, 31B05, 60J75, 35K90 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 [CDV22]. 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. |
| title | Semiconvexity estimates for nonlinear integro-differential equations |
| topic | Analysis of PDEs 47G20, 35B65, 31B05, 60J75, 35K90 |
| url | https://arxiv.org/abs/2306.16751 |