765 articles – 1378 references  [version française]
 HAL: hal-00281623, version 1
 Advances in Differential Equations 11, 2 (2006) 201-240
 Perturbation, Interpolation, and Maximal Regularity
 Bernhard H. Haak 1, 2, Markus Haase 3
 (2006)
 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
 Keyword(s): perturbation – sectoriality – $R$-sectoriality
 hal-00281623, version 1 http://hal.archives-ouvertes.fr/hal-00281623 oai:hal.archives-ouvertes.fr:hal-00281623 From: Bernhard Hermann Haak <> Submitted on: Friday, 23 May 2008 14:53:14 Updated on: Thursday, 3 July 2008 13:28:48