HAAK, Bernhard H.; HAASE, Markus; KUNSTMANN, Peer Christian

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HAAK, Bernhard H.
INSTITUT FUER ANALYSIS
Institut de Mathématiques de Bordeaux [IMB]

HAASE, Markus
Classe di Scienze

KUNSTMANN, Peer Christian
INSTITUT FUER ANALYSIS

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Ce document a été publié dans

Advances in Differential Equations. 2006, vol. 11, n° 2, p. 201-240

Khayyam Publishing

Résumé en anglais

We prove perturbation theorems for sectoriality and $R$--sectoriality in Banach spaces, which yield results on perturbation of generators of analytic semigroups and on perturbation of maximal $L^p$--regularity. For a given sectorial or $R$--sectorial operator $A$ in a Banach space $X$ we give conditions on intermediate spaces $Z$ and $W$ such that, for an operator $S: Z\to W$ of small norm, the perturbed operator $A+S$ is again sectorial or $R$--sectorial, respectively. These conditions are obtained by factorising the perturbation as $S= -BC$, where $B$ acts on an auxiliary Banach space $Y$ and $C$ maps into $Y$. Our results extend previous work on perturbations in the scale of fractional domain spaces associated with $A$ and allow for a greater flexibility in choosing intermediate spaces for the action of perturbation operators. At the end we illustrate our results with several examples, in particular with an application to a rough boundary value problem.< Réduire

Mots clés en anglais

perturbation

sectoriality

$R$-sectoriality

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Perturbation, Interpolation, and Maximal Regularity

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