The heat equation with rough boundary conditions and holomorphic functional calculus

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 L^p-spaces for power weights which fall outside the classical class of A_p-weights. Furthermore, we characterize the domain of the operator and derive...

Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions

In this paper, we establish weighted L^q–L^p-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the optimal regularity of the initial-boundary...