Higher-order derivative estimates for the heat equation on a smooth domain
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908308604977152 |
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| author | Furuto, Yoshinori Iwabuchi, Tsukasa |
| author_facet | Furuto, Yoshinori Iwabuchi, Tsukasa |
| contents | We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases $p = 1, \infty$. We also obtain derivative estimates for the equation with the fractional Dirichlet Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order derivative estimates for the heat equation on a smooth domain Furuto, Yoshinori Iwabuchi, Tsukasa Analysis of PDEs Functional Analysis We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases $p = 1, \infty$. We also obtain derivative estimates for the equation with the fractional Dirichlet Laplacian. |
| title | Higher-order derivative estimates for the heat equation on a smooth domain |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2504.06510 |