Maximal regularity for parabolic equations with measurable dependence on time and applications

The subject of this thesis is the study of maximal L^p-regularity of the Cauchy problem u'(t)+A(t)u(t)=f(t), t∈ (0,T), u(0)=x. <br/>We assume (A(t))_{t∈ (0,T)} to be a family of closed operators on a Banach space X₀, with constant domain D(A(t))=X₁ for every t∈ (0,T). Maximal L^p-regularity means that...

Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time

In this paper we study maximal Lp-regularity for evolution equations with time-dependent operators A. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the Lp-boundedness of a class of vector-valued singular integrals which does not rely on Hörmander conditions in the time...

Maximal Lp-Regularity for Stochastic Evolution Equations

R -bounded Representations of L 1 ( G )