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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.18402 |
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| _version_ | 1866909991766589440 |
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| author | Hernández, Joan |
| author_facet | Hernández, Joan |
| contents | In this paper we study removable singularities for regular $(1,\frac{1}{2s})$-Lipschitz solutions of the $s$-fractional heat equation for $1/2<s<1$. To do so, we define a Lipschitz fractional caloric capacity and study its critical dimension and the $L^2$-boundedness of a pair of singular integral operators, whose kernels will be the gradient of the fundamental solution of the fractional heat equation and its conjugate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Removable singularities for Lipschitz fractional caloric functions in time varying domains Hernández, Joan Analysis of PDEs In this paper we study removable singularities for regular $(1,\frac{1}{2s})$-Lipschitz solutions of the $s$-fractional heat equation for $1/2<s<1$. To do so, we define a Lipschitz fractional caloric capacity and study its critical dimension and the $L^2$-boundedness of a pair of singular integral operators, whose kernels will be the gradient of the fundamental solution of the fractional heat equation and its conjugate. |
| title | Removable singularities for Lipschitz fractional caloric functions in time varying domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.18402 |