Staffans–Weiss perturbations for maximal $$L^p$$-regularity in Banach spaces

Abstract

In this paper, we show that the concept of maximal \(L^p\)-regularity is stable under a large class of unbounded perturbations, namely Staffans–Weiss perturbations. To that purpose, we first prove that the analyticity of semigroups is preserved under this class of perturbations, which is a necessary condition for the maximal regularity. In UMD spaces, \({\mathcal {R}}\)-boundedness is exploited to give conditions guaranteeing the maximal regularity. For Banach spaces, a condition is imposed to prove maximal regularity. Moreover, we apply the obtained results to perturbed boundary value problems.