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 language | English |
---|---|
Pages (from-to) | 5832-5899 |
Number of pages | 68 |
Journal | Journal of Differential Equations |
Volume | 269 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Functional calculus of the Laplace operator
- Heat equation with inhomogeneous Dirichlet boundary conditions
- Maximal regularity
- Mixed-norms
- Traces
- Weights