Advances in Differential Equations
- Adv. Differential Equations
- Volume 11, Number 2 (2006), 201-240.
Perturbation, interpolation, and maximal regularity
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.
Adv. Differential Equations Volume 11, Number 2 (2006), 201-240.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35K90: Abstract parabolic equations 46B70: Interpolation between normed linear spaces [See also 46M35] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Haak, Bernhard H.; Haase, Markus; Kunstmann, Peer C. Perturbation, interpolation, and maximal regularity. Adv. Differential Equations 11 (2006), no. 2, 201--240.https://projecteuclid.org/euclid.ade/1355867717