The heat equation with rough boundary conditions and holomorphic functional calculus

Journal article (2020)

Authors

N. Lindemulder Analysis - EEMCS , Karlsruhe Institut für Technologie
M.C. Veraar Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2020 N. Lindemulder, M.C. Veraar
DOI: https://doi.org/10.1016/j.jde.2020.04.023
Weights Maximal regularity Mixed-norms Traces Functional calculus of the Laplace operator Heat equation with inhomogeneous Dirichlet boundary conditions
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Published Date

2020

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.