On the Lipschitz continuity of the heat kernel
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910299043397632 |
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| author | Bifulco, Patrizio Mugnolo, Delio |
| author_facet | Bifulco, Patrizio Mugnolo, Delio |
| contents | We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for Hölder or Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and quantum graphs, to Laplacians on a class of fractals including the Sierpiński gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08889 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Lipschitz continuity of the heat kernel Bifulco, Patrizio Mugnolo, Delio Functional Analysis 47B34, 47D06, 47G10, 35K90 We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for Hölder or Lipschitz continuity of the kernels. We apply our results to (pseudo)differential operators on domains and quantum graphs, to Laplacians on a class of fractals including the Sierpiński gasket, and to structurally damped wave equations. An extension to non-autonomous problems is also discussed. |
| title | On the Lipschitz continuity of the heat kernel |
| topic | Functional Analysis 47B34, 47D06, 47G10, 35K90 |
| url | https://arxiv.org/abs/2307.08889 |