The heat equation with rough boundary conditions and holomorphic functional calculus

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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.

Original languageEnglish
Pages (from-to)5832-5899
Number of pages68
JournalJournal of Differential Equations
Volume269
Issue number7
DOIs
Publication statusPublished - 2020

Keywords

  • Functional calculus of the Laplace operator
  • Heat equation with inhomogeneous Dirichlet boundary conditions
  • Maximal regularity
  • Mixed-norms
  • Traces
  • Weights

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