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The heat equation with rough boundary conditions and holomorphic functional calculus

Journal Article (2020)
Author(s)

Nick Lindemulder (TU Delft - Electrical Engineering, Mathematics and Computer Science, Karlsruhe Institut für Technologie)

Mark Veraar (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group
Analysis
DOI related publication
https://doi.org/10.1016/j.jde.2020.04.023 Final published version
More Info
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Publication Year
2020
Language
English
Research Group
Analysis
Issue number
7
Volume number
269
Pages (from-to)
5832-5899
Downloads counter
197
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Institutional Repository
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Abstract

In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded H∞-calculus on weighted Lp-spaces for power weights which fall outside the classical class of Ap-weights. Furthermore, we characterize the domain of the operator and derive several consequences on elliptic and parabolic regularity. In particular, we obtain a new maximal regularity result for the heat equation with rough inhomogeneous boundary data.