Higher-order derivative estimates for the heat equation on a smooth domain

Yoshinori Furuto; Tsukasa Iwabuchi

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arXiv · 2504.06510

Higher-order derivative estimates for the heat equation on a smooth domain

Yoshinori Furuto·Tsukasa Iwabuchi

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Abstract

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.

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Yoshinori Furuto, Tsukasa Iwabuchi. 2025-04-09. Higher-order derivative estimates for the heat equation on a smooth domain. https://arxiv.org/abs/2504.06510

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