English

$L^p$ 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 p=1,p = 1, \infty.

Keywords

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}
}

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12 pages