Maximal L_{p} regularity for degenerate parabolic problems

Frank Weber Universität Zürich Mathematisches Institut Winterthurerstrasse 190 CH - 8057 Zürich Switzerland

                  fweber@math.unizh.ch

Maximal regularity for linear parabolic problems plays an essential role for the treatment of nonlinear applications.

The aim is to present a method to prove maximal regularity for degenerate parabolic problems in X = L_{p} ((0, T), E) with p ∈ (1, ∞) , where E denotes a UMD Banach space. The abstract approach combines Dore-Venni type theorems on operator sums with results on products of non-commuting sectorial operators which possess bounded imaginary powers in X.