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

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.

arXiv commentarXiv admin note: text overlap with arXiv:2405.06300