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On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications

Published online by Cambridge University Press:  20 March 2008

Lars Diening ,
Josef Málek  and
Mark Steinhauer
Lars Diening
Affiliation:
Abteilung für Angewandte Mathematik, Universität Freiburg, Eckerstr. 1, 79104 Freiburg i. Br., Germany; diening@mathematik.uni-freiburg.de
Josef Málek
Affiliation:
Mathematical Institute, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic; malek@karlin.mff.cuni.cz
Mark Steinhauer
Affiliation:
Mathematical Seminar, University of Bonn, Nussallee 15, 53115 Bonn, Germany; MSteinh@uni-bonn.de
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Abstract

We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in [Frehse et al., SIAM J. Math. Anal34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.

Keywords

Lipschitz truncation of $W^{1,p}_0/W^{1,p(\cdot)}_0$-functionsexistenceweak solutionincompressible fluidpower-law fluidelectro-rheological fluid
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 2 , April 2008 , pp. 211 - 232
Copyright
© EDP Sciences, SMAI, 2008

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