$L^p$ estimate of the heat equation on a bounded domain

Fuente: arXiv
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Main Authors: Furuto, Yoshinori, Iwabuchi, Tsukasa, Kohama, Ryusei
Format: Preprint
Published: 2024
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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