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

Lars Diening; Josef Málek; Mark Steinhauer

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 2, page 211-232
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Diening, Lars, Málek, Josef, and Steinhauer, Mark. "On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 211-232. <http://eudml.org/doc/250332>.

@article{Diening2008,
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. },
author = {Diening, Lars, Málek, Josef, Steinhauer, Mark},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Lipschitz truncation of $W^\{1,p\}_0/W^\{1,p(\cdot)\}_0$-functions; existence; weak solution; incompressible fluid; power-law fluid; electro-rheological fluid; Lipschitz truncation of -functions},
language = {eng},
month = {3},
number = {2},
pages = {211-232},
publisher = {EDP Sciences},
title = {On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications},
url = {http://eudml.org/doc/250332},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Diening, Lars
AU - Málek, Josef
AU - Steinhauer, Mark
TI - On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/3//
PB - EDP Sciences
VL - 14
IS - 2
SP - 211
EP - 232
AB - 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.
LA - eng
KW - Lipschitz truncation of $W^{1,p}_0/W^{1,p(\cdot)}_0$-functions; existence; weak solution; incompressible fluid; power-law fluid; electro-rheological fluid; Lipschitz truncation of -functions
UR - http://eudml.org/doc/250332
ER -

References

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