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2006 Perturbation, interpolation, and maximal regularity
Bernhard H. Haak, Markus Haase, Peer C. Kunstmann
Adv. Differential Equations 11(2): 201-240 (2006).

Abstract

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.

Citation

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Bernhard H. Haak. Markus Haase. Peer C. Kunstmann. "Perturbation, interpolation, and maximal regularity." Adv. Differential Equations 11 (2) 201 - 240, 2006.

Information

Published: 2006
First available in Project Euclid: 18 December 2012

zbMATH: 1110.47032
MathSciNet: MR2194499

Subjects:
Primary: 47A55
Secondary: 34G10, 35K90, 46B70, 47D06

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.11 • No. 2 • 2006
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