Elliptic and Parabolic Equations - Abstract

Amann, Herbert

Parabolic systems on singular manifolds

We describe a maximal regularity theorem for general parabolic systems on non smooth manifolds having corners, edges, conical points, cracks etc., on the boundary and in the interior. Its proof is based on a localization method reducing the problem to an infinite coupled system of boundary value problems and on maximal regularity results for parabolic systems on all of $mathbb R^n$ and half spaces.