R-Boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators

  • It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class (HT ) and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms of pseudodifferential operators with R-bounded symbols, yielding by an iteration argument the R-boundedness of λ(A − λ)−1 in R(λ)≥ τ for some τ ∈ IR. To this end, elements of a symbolic and operator calculus of pseudodifferential operators with R-bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on Rd with operator valued coefficients.

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Metadaten
Author details:Robert Denk, Thomas KrainerGND
URN:urn:nbn:de:kobv:517-opus-30147
Publication series (Volume number):Preprint ((2006) 14)
Publication type:Preprint
Language:English
Publication year:2006
Publishing institution:Universität Potsdam
Release date:2009/05/05
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J70 Degenerate elliptic equations
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Kxx Thin bodies, structures / 74K20 Plates
Collection(s):Universität Potsdam / Schriftenreihen / Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis
Universität Potsdam / Schriftenreihen / Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis / 2006
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
External remark:
Die Printversion kann in der Universitätsbibliothek Potsdam eingesehen werden:
Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partielle Differentialgleichungen und Komplexe Analysis, 1997-

Die Online-Fassung wird auf der Homepage des Instituts für Mathematik veröffentlicht.

RVK-KLassifikation: SI 990
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