$L^p$ estimate of the heat equation on a bounded domain
Analysis of PDEs
2024-05-13 v1
Abstract
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 .
Cite
@article{arxiv.2405.06300,
title = {$L^p$ estimate of the heat equation on a bounded domain},
author = {Yoshinori Furuto and Tsukasa Iwabuchi and Ryusei Kohama},
journal= {arXiv preprint arXiv:2405.06300},
year = {2024}
}
Comments
12 pages