Operator Theory: Advances and Applications

General Parabolic Mixed Order Systems in Lp and Applications

Authors: Denk, Robert, Kaip, Mario

  • General approach to non-standard parabolic equations and systems
  • Unified treatment in several types of non-integer Lp-Sobolev spaces
  • Applicable to a large class of equations, e.g. to free boundary value problems and to equations in fluid dynamics and thermoelasticity ​
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About this book

In this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The last-mentioned class appears in a natural way as traces of Lp-Lq-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier–Stokes equations with Boussinesq–Scriven surface, and the Lp-Lq two-phase Stefan problem with Gibbs–Thomson correction.​

Table of contents (5 chapters)

  • Introduction and Outline

    Denk, Robert (et al.)

    Pages 1-10

  • The joint time-space H ∞-calculus

    Denk, Robert (et al.)

    Pages 11-67

  • The Newton polygon approach for mixed-order systems

    Denk, Robert (et al.)

    Pages 69-141

  • Triebel-Lizorkin spaces and the L p -L q -setting

    Denk, Robert (et al.)

    Pages 143-185

  • Application to parabolic differential equations

    Denk, Robert (et al.)

    Pages 187-228

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-02000-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-01999-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-319-37592-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
General Parabolic Mixed Order Systems in Lp and Applications
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
239
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02000-6
DOI
10.1007/978-3-319-02000-6
Hardcover ISBN
978-3-319-01999-4
Softcover ISBN
978-3-319-37592-2
Series ISSN
0255-0156
Edition Number
1
Number of Pages
VIII, 250
Number of Illustrations and Tables
15 b/w illustrations, 1 illustrations in colour
Topics