Dirichlet heat kernel estimates for parabolic nonlocal equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918226093408256 |
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| author | Svinger, Philipp Weidner, Marvin |
| author_facet | Svinger, Philipp Weidner, Marvin |
| contents | In this article we establish the optimal $C^s$ boundary regularity for solutions to nonlocal parabolic equations in divergence form in $C^{1,α}$ domains and prove a higher order boundary Harnack principle in this setting. Our approach applies to a broad class of nonlocal operators with merely Hölder continuous coefficients, but our results are new even in the translation invariant case. As an application, we obtain sharp two-sided estimates for the associated Dirichlet heat kernel. Notably, our estimates cover nonlocal operators with time-dependent coefficients, which had remained open in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirichlet heat kernel estimates for parabolic nonlocal equations Svinger, Philipp Weidner, Marvin Analysis of PDEs 47G20, 35B65, 35K08 In this article we establish the optimal $C^s$ boundary regularity for solutions to nonlocal parabolic equations in divergence form in $C^{1,α}$ domains and prove a higher order boundary Harnack principle in this setting. Our approach applies to a broad class of nonlocal operators with merely Hölder continuous coefficients, but our results are new even in the translation invariant case. As an application, we obtain sharp two-sided estimates for the associated Dirichlet heat kernel. Notably, our estimates cover nonlocal operators with time-dependent coefficients, which had remained open in the literature. |
| title | Dirichlet heat kernel estimates for parabolic nonlocal equations |
| topic | Analysis of PDEs 47G20, 35B65, 35K08 |
| url | https://arxiv.org/abs/2512.01919 |