Type of Publication:  Monograph 
Author:  Denk, Robert; Kaip, Mario 
Year of publication:  2013 
Publishing House:  Basel : Birkhäuser 
ISBN:  9783319019994 
Series:  Operator Theory: Advances and Applications;239 
DOI (citable link):  https://dx.doi.org/10.1007/9783319020006 
Summary: 
In this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixedorder systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show wellposedness in LpLqSobolev 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 noninteger LpSobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The lastmentioned class appears in a natural way as traces of LpLqSobolev spaces. We also present a selection of applications in the whole space and on halfspaces. Among others, we prove wellposedness of the linearizations of the generalized thermoelastic plate equation, the twophase Navier–Stokes equations with Boussinesq–Scriven surface, and the LpLq twophase Stefan problem with Gibbs–Thomson correction.

MSC Classification:  35R35, 3502, 35K40, 35Q30, 35Q79, 76T10 
Subject (DDC):  510 Mathematics 
Keywords:  Newtonpolygon, TriebelLizorkin spaces, free boundary problems, mixed order systems, parabolic differential equations 
Bibliography of Konstanz:  Yes 
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DENK, Robert, Mario KAIP, 2013. General Parabolic Mixed Order Systems in L_{p} and Applications. Basel : Birkhäuser. ISBN 9783319019994. Available under: doi: 10.1007/9783319020006
@book{Denk2013Gener25670, isbn={9783319019994}, publisher={Basel : Birkhäuser}, series={Operator Theory: Advances and Applications;239}, title={General Parabolic Mixed Order Systems in L_{p} and Applications}, year={2013}, doi={10.1007/9783319020006}, author={Denk, Robert and Kaip, Mario} }