Staffans–Weiss perturbations for maximal Lp-regularity in Banach spaces

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 co...

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Bibliographic Details
Published in:Journal of evolution equations 2022, Vol.22 (1)
Main Authors: Amansag, Ahmed, Bounit, Hamid, Driouich, Abderrahim, Hadd, Said
Format: Article
Language:English
Subjects:
Analysis
Banach spaces
Boundary value problems
Mathematics
Mathematics and Statistics
Perturbation
Regularity
Online Access:Get full text
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Summary: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, 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.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-022-00779-6