MAXIMAL REGULARITY FOR ABSTRACT PARABOLIC PROBLEMS WITH INHOMOGENEOUS BOUNDARY DATA IN Lp-SPACES
نویسنده
چکیده
Several abstract model problems of elliptic and parabolic type with inhomogeneous 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.
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