Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in $L_p$-spaces

Abstract

Several abstract model problems of elliptic and parabolic type with inhomoge-neous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem , real and complex interpolation, and trace theorems, optimal Lp-regularity is shown. By means of this purely operator theoretic approach, classical results on Lp-regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface diffusion for the diffusion equation is included.