The parabolic Harnack inequality for nonlocal equations
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913208020762624 |
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| author | Kassmann, Moritz Weidner, Marvin |
| author_facet | Kassmann, Moritz Weidner, Marvin |
| contents | We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and Hölder regularity estimates. We discuss in detail the shortcomings of previous results in this direction. The key element of our approach is a fine study of the nonlocal tail term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05975 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The parabolic Harnack inequality for nonlocal equations Kassmann, Moritz Weidner, Marvin Analysis of PDEs Probability 47G20, 35B65, 31B05, 60J75, 35K90 We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable coefficients. Within the variational framework we prove the parabolic Harnack inequality and Hölder regularity estimates. We discuss in detail the shortcomings of previous results in this direction. The key element of our approach is a fine study of the nonlocal tail term. |
| title | The parabolic Harnack inequality for nonlocal equations |
| topic | Analysis of PDEs Probability 47G20, 35B65, 31B05, 60J75, 35K90 |
| url | https://arxiv.org/abs/2303.05975 |