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hal-00281623, version 1

## Perturbation, Interpolation, and Maximal Regularity

Bernhard H. Haak 12, Markus Haase 3, Peer Christian Kunstmann 1

Advances in Differential Equations 11, 2 (2006) 201-240

Résumé : 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.

• 1 :  INSTITUT FUER ANALYSIS
• Université de Karlsruhe (TH)
• 2 :  Institut de Mathématiques de Bordeaux (IMB)
• CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
• 3 :  Classe di Scienze
• Scuola Normale Superiore
• Mots-clés : perturbation – sectoriality – $R$-sectoriality

• hal-00281623, version 1
• oai:hal.archives-ouvertes.fr:hal-00281623
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• Soumis le : Vendredi 23 Mai 2008, 14:53:14
• Dernière modification le : Jeudi 3 Juillet 2008, 13:28:48