Equivalence of definitions of fractional caloric functions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918453351284736 |
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| author | Rutkowski, Artur |
| author_facet | Rutkowski, Artur |
| contents | We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $α$-stable process. We also provide sufficient conditions for the boundary and exterior data under which the solutions are classical and we give off-diagonal estimates for the derivatives of the Dirichlet heat kernel and the lateral Poisson kernel, which might be of their own interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence of definitions of fractional caloric functions Rutkowski, Artur Analysis of PDEs Probability 35S16, 35C15, 35D30 We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $α$-stable process. We also provide sufficient conditions for the boundary and exterior data under which the solutions are classical and we give off-diagonal estimates for the derivatives of the Dirichlet heat kernel and the lateral Poisson kernel, which might be of their own interest. |
| title | Equivalence of definitions of fractional caloric functions |
| topic | Analysis of PDEs Probability 35S16, 35C15, 35D30 |
| url | https://arxiv.org/abs/2410.16188 |