Elliptic and Parabolic Equations - Abstract

Griepentrog, Jens A.

Maximal regularity for nonsmooth parabolic boundary value problems in Sobolev--Morrey spaces

In our talk we present maximal regularity results for second order parabolic boundary value problems on Lipschitz domains of arbitrary space dimension, with nonsmooth coefficients and inhomogeneous mixed boundary conditions. Even under these general assumptions this class of initial boundary value problems generates isomorphisms between two suitable scales of Sobolev--Morrey spaces for solutions and right hand sides. Moreover, the solutions are Hölder continuous in time and space up to the boundary, and they depend smoothly on the data of the problem, which makes it possible to generalize the results to quasilinear parabolic problems.