Maximal regularity for non-autonomous Schroedinger type equations

Details Maximal regularity for non-autonomous Schroedinger type equations Maximal regularity for non-autonomous Schroedinger type equations

2009-06-12

arxiv.org/abs/0906.2294v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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 $m$.

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