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

2025/04/09 by Furuto, Yoshinori, Iwabuchi, Tsukasa · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2504.06510

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, ∞. We also obtain derivative estimates for the equation with the fractional Dirichlet Laplacian.

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• Mean field control with absorption

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