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.
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Amansag, A., Bounit, H., Driouich, A. et al. Staffans–Weiss perturbations for maximal \(L^p\)-regularity in Banach spaces. J. Evol. Equ. 22, 15 (2022). https://doi.org/10.1007/s00028-022-00779-6
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DOI: https://doi.org/10.1007/s00028-022-00779-6