Anisotropic function spaces and maximal regularity for parabolic problems. Part 1

Abstract

In this first part of a treatise on maximal regularity for linear parabolic systems we provide an in-depth investigation of anisotropic function spaces. Special attention is given to trace and extension theorems on hyper-planes and corners. Building on these results, parabolic evolution equations in strong and weak settings will be studied in Part 2.