Maximal regularity for non-autonomous Schrödinger type equations

El Maati Ouhabaz (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper we study the maximal regularity property for nonautonomous evolution equations ∂tu(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 Hölder continuity assumption of t → a(t, *,*). In the non-Hilbert space situation we focus on Schrödinger type operators A(t) := − + m(t, *) and prove Lp − Lq estimates for a wide class of time and space dependent

Mots clés: Maximal Lp − Lq regularity Non-autonomous Cauchy problems Schrödinger operators

Domaines: Equations aux dérivées partielles [math.AP]

El Maati Ouhabaz. Maximal regularity for non-autonomous Schrödinger type equations. Journal of Differential Equations, 2010, 248, pp.1668-1683. ⟨10.1016/j.jde.2009.10.004⟩. ⟨hal-00998109⟩