Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909220628070400 |
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| author | Byun, Sun-Sig Kim, Kyeongbae Kumar, Deepak |
| author_facet | Byun, Sun-Sig Kim, Kyeongbae Kumar, Deepak |
| contents | We prove Calderón-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of fractional Laplacian type data and a non-divergence type data. Interestingly, even though the kernel coefficients are discontinuous, we obtain a significant increment of fractional differentiability for the solutions, which is not observed in the corresponding local parabolic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01654 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients Byun, Sun-Sig Kim, Kyeongbae Kumar, Deepak Analysis of PDEs We prove Calderón-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of fractional Laplacian type data and a non-divergence type data. Interestingly, even though the kernel coefficients are discontinuous, we obtain a significant increment of fractional differentiability for the solutions, which is not observed in the corresponding local parabolic equations. |
| title | Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.01654 |