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General parabolic mixed order systems in Lp and applications / Robert Denk, Mario Kaip.



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Denk, Robert, 1964- author.
Publication date:
[Basel] : Birkhäuser ; Cham : Springer, [2013]
  • Book
  • viii, 250 pages : illustrations ; 25 cm.
Includes bibliographical references (pages 231-238) and index.
  • The joint time-space H(infinity)-calculus
  • The joint H(infinity)-calculus for tuples of operators
  • Sectorial and bisectorial operators, R-boundedness
  • Joint H(infinity)-calculus
  • Vector-valued Sobolev spaces
  • Interpolation of Banach spaces
  • Retractions and coretractions
  • Definition of Sobolev spaces
  • The time-space derivative
  • Fourier multipliers
  • Vector-valued space and time derivatives
  • Joint space-time H(infinity)-calculus
  • The Newton polygon approach for mixed-order systems
  • Inhomogeneous symbols and the Newton polygon
  • Inhomogeneous symbols and principal parts
  • Newton polygons and order functions
  • N-parameter-ellipticity and N-parabolicity
  • N-parameter-elliptic symbols and Sn(Lt x Lx)
  • Partition of the co-variable space
  • Equivalent characterization of Sn(Lt x Lx)
  • H(infinity)-calculus of N-parabolic mixed-order systems
  • The H(infinity)-calculus of N-parabolic symbols
  • Mixed-order systems on spaces of mixed scales
  • Remarks on the compatibility condition
  • Triebel-Lizorkin spaces and the Lp-Lq-setting
  • Vector-valued Triebel-Lizorkin spaces and interpolation
  • Anisotropic Triebel-Lizorkin spaces and representation by intersections
  • Auxiliary results on Bessel-valued Triebel-Lizorkin spaces
  • The joint time-space H(infinity)-calculus on Bessel-valued Triebel-Lizorkin spaces
  • H(infinity)-calculus of N-parabolic symbols on Bessel-valued Triebel-Lizorkin spaces
  • Mixed-order systems on Triebel-Lizorkin spaces
  • Singular integral operators on Lp-Lq
  • Singular integral operators
  • Extension symbols
  • Application to parabolic differential equations
  • The generalized Lp-Lq Stokes problem on ...
  • Remarks on homogeneous Sobolev spaces
  • The generalized Stokes problem
  • The generalized Lp-Lq thermo-elastic plate equations on ...
  • A linear Lp-Lq Cahn-Hilliard-Gurtin problem in ...
  • A compressible fluid model of Korteweg type on ...
  • A linear three-phase problem on ...
  • The spin-coating process
  • Two-phase Navier-Stokes equations with Boussinesq-Scriven surface and gravity
  • The Lp-Lq two-phase Stefan problem with Gibbs-Thomson correction
  • List of figures
  • Bibliography
  • List of symbols
  • Index.
Kaip, Mario, author.
Available in another form:
9783319020006 (online)
Operator theory, advances and applications, 0255-0156 ; volume 239
Operator theory, advances and applications ; 239.

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