Lions’ maximal regularity problem for non-autonomous evolution equations

Abstract

The aim of this talk is to discuss some recent progress on a problem of J.L. Lions concerning maximal regularity for evolution equations

Unlike the autonomous case (where $A\left(t\right)=A$) in which one always has maximal regularity in the Hilbert space setting, the non-autonomous equations may not enjoy this property. We describe some positive and negative results on this problem.