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

Denk, Robert; Krainer, Thomas

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

Dateien

preprint_217.pdfGröße: 285.83 KBDownloads: 270

Datum

2006

Autor:innen

Denk, Robert

Krainer, Thomas

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

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 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 the resolvent in a closed complex half-plane. 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 with operator valued coefficients.

Fachgebiet (DDC)

004 Informatik

Zitieren

ISO 690

DENK, Robert, Thomas KRAINER, 2006. R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators

BibTex

@unpublished{Denk2006Rboun-538,
  year={2006},
  title={R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators},
  author={Denk, Robert and Krainer, Thomas}
}

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