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arXiv · 2003.02123

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

A. Amansag·H. Bounit·A. Driouich·S. Hadd
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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 conditions are exploited to give conditions guaranteing the maximal regularity. For non-reflexive Banach space, a condition is imposed to the Dirichlet operator associated to the boundary value problem to prove the maximal regularity. A Pde example illustrating the theory and an application to a class of non-autonomous perturbed boundary value problems are presented.

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A. Amansag, H. Bounit, A. Driouich, S. Hadd. 2020-03-02. Staffans-Weiss perturbations for Maximal $L^p$-regularity in Banach spaces. https://arxiv.org/abs/2003.02123

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