The heat equation with rough boundary conditions and holomorphic functional calculus
N. Lindemulder (TU Delft - Analysis, Karlsruhe Institut für Technologie)
Mark C. Veraar (TU Delft - Analysis)
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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.
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