Extrapolation of $L^p$ maximal regularity for second order Cauchy problems

Maximal Regularity of Discrete Second Order Cauchy Problems in Banach Spaces

We characterize the discrete maximal regularity for second order difference equations by means of spectral and R-boundedness properties of the resolvent set.

On the maximal Lp-regularity of parabolic mixed order systems

We study maximal Lp-regularity for a class of pseudodifferential mixed order systems on a space-time cylinder R×R or X×R, where X is a closed smooth manifold. To this end we construct a calculus of Volterra pseudodifferential operators and characterize the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms between suit...

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Semilinear Evolution Equations of Second Order via Maximal Regularity

Almost Periodic Solutions of First- and Second-Order Cauchy Problems

Almost periodicity of solutions of firstand second-order Cauchy problems on the real line is proved under the assumption that the imaginary (resp. real) spectrum of the underlying operator is countable. Related results have been obtained by Ruess Vu~ and Basit. Our proof uses a new idea. It is based on a factorisation method which also gives a short proof (of the vector-valued version) of Loomi...