Volume 14, Number 2, April-June 2008
|Page(s)||211 - 232|
|Published online||20 March 2008|
On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
Abteilung für Angewandte Mathematik, Universität Freiburg, Eckerstr. 1,
79104 Freiburg i. Br., Germany; firstname.lastname@example.org
2 Mathematical Institute, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic; email@example.com
3 Mathematical Seminar, University of Bonn, Nussallee 15, 53115 Bonn, Germany; MSteinh@uni-bonn.de
Revised: 25 August 2006
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. Anal 34 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.
Mathematics Subject Classification: 35J55 / 35J65 / 35J70 / 35Q35 / 76D99
Key words: Lipschitz truncation of W01,p/W01,p(·)-functions / existence / weak solution / incompressible fluid / power-law fluid / electro-rheological fluid
© EDP Sciences, SMAI, 2008
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