rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: General Parabolic Mixed Order Systems in Lp and Applications
  name:
    name part: Denk, Robert.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kaip, Mario.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 250 p. 16 illus., 1 illus. in color. online resource.
  abstract: 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 that 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 latter 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: Introduction and Outline -- 1 The joint time-space H(infinity)-calculus -- 2 The Newton polygon approach for mixed-order systems.-3 Triebel-Lizorkin spaces and the Lp-Lq setting.- 4 Application to parabolic differential equations -- List of figures.-Bibliography -- List of symbols -- Index.
  note: by Robert Denk, Mario Kaip.
  subject:
    topic: Mathematics
  subject:
    topic: Operator theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Mathematical Physics
  subject:
    topic: Operator Theory
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Operator Theory: Advances and Applications, 239
  identifier: 9783319020006
  identifier: http://dx.doi.org/10.1007/978-3-319-02000-6
  record info:
    record creation date: 131122
    record change date: 20151103121559.0
    record identifier: 978-3-319-02000-6