Higher-order derivative estimates for the heat equation on a smooth domain (2504.06510v1)

Published 9 Apr 2025 in math.AP and math.FA

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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