$L^p$ estimate of the heat equation on a bounded domain
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914790506496000 |
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| author | Furuto, Yoshinori Iwabuchi, Tsukasa Kohama, Ryusei |
| author_facet | Furuto, Yoshinori Iwabuchi, Tsukasa Kohama, Ryusei |
| contents | We consider the linear heat equation on a bounded domain. We study estimates of the derivatives, up to the second order, of the solution locally in time in the Lebesgue spaces. We give a self-contained proof of the estimates in the end-point cases $p = 1, \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$ estimate of the heat equation on a bounded domain Furuto, Yoshinori Iwabuchi, Tsukasa Kohama, Ryusei Analysis of PDEs 35K05, 35K08 We consider the linear heat equation on a bounded domain. We study estimates of the derivatives, up to the second order, of the solution locally in time in the Lebesgue spaces. We give a self-contained proof of the estimates in the end-point cases $p = 1, \infty$. |
| title | $L^p$ estimate of the heat equation on a bounded domain |
| topic | Analysis of PDEs 35K05, 35K08 |
| url | https://arxiv.org/abs/2405.06300 |