General Parabolic Mixed Order Systems in Lp and Applications by Robert DenkGeneral Parabolic Mixed Order Systems in Lp and Applications by Robert Denk

General Parabolic Mixed Order Systems in Lp and Applications

byRobert Denk, Mario Kaip

Hardcover | December 10, 2013

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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 inLp-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-integerLp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel-Lizorkin spaces. The last-mentioned class appears in a natural way as traces ofLp-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 theLp-Lqtwo-phase Stefan problem with Gibbs-Thomson correction.
Title:General Parabolic Mixed Order Systems in Lp and ApplicationsFormat:HardcoverDimensions:250 pagesPublished:December 10, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319019996

ISBN - 13:9783319019994


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.