Perturbation, Interpolation, and Maximal Regularity
| hal.structure.identifier | INSTITUT FUER ANALYSIS | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard H. | |
| hal.structure.identifier | Classe di Scienze | |
| dc.contributor.author | HAASE, Markus | |
| hal.structure.identifier | INSTITUT FUER ANALYSIS | |
| dc.contributor.author | KUNSTMANN, Peer Christian | |
| dc.date.accessioned | 2024-04-04T02:53:02Z | |
| dc.date.available | 2024-04-04T02:53:02Z | |
| dc.date.issued | 2006 | |
| dc.identifier.issn | 1079-9389 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192133 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Khayyam Publishing | |
| dc.subject.en | perturbation | |
| dc.subject.en | sectoriality | |
| dc.subject.en | $R$-sectoriality | |
| dc.title.en | Perturbation, Interpolation, and Maximal Regularity | |
| dc.type | Article de revue | |
| bordeaux.journal | Advances in Differential Equations | |
| bordeaux.page | 201-240 | |
| bordeaux.volume | 11 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00281623 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00281623v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Differential%20Equations&rft.date=2006&rft.volume=11&rft.issue=2&rft.spage=201-240&rft.epage=201-240&rft.eissn=1079-9389&rft.issn=1079-9389&rft.au=HAAK,%20Bernhard%20H.&HAASE,%20Markus&KUNSTMANN,%20Peer%20Christian&rft.genre=article |
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