Maximal regularity for non-autonomous Schroedinger type equations

Abstract

In this paper we study the maximal regularity property for non-autonomous evolution equations ${\partial }_{t}u(t)+A(t)u(t)=f(t),u(0)=0.$ If the equation is considered on a Hilbert space $H$ and the operators $A(t)$ are defined by sesquilinear forms $a(t,.,.)$ we prove the maximal regularity under a Holder continuity assumption of $t\to a(t,.,.)$. In the non-Hilbert space situation we focus on Schrodinger type operators $A(t):=-\Delta +m(t,.)$ and prove $L^p-L^q$ estimates for a wide class of time and space dependent potentials $m$.

16 pages