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.
Mots-clés : Lipschitz truncation of
@article{COCV_2008__14_2_211_0,
author = {Steinhauer, Mark and M\'alek, Josef and Diening, Lars},
title = {On {Lipschitz} truncations of {Sobolev} functions (with variable exponent) and their selected applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {211--232},
publisher = {EDP-Sciences},
volume = {14},
number = {2},
year = {2008},
doi = {10.1051/cocv:2007049},
mrnumber = {2394508},
zbl = {1143.35037},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2007049/}
}
TY - JOUR AU - Steinhauer, Mark AU - Málek, Josef AU - Diening, Lars TI - On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 211 EP - 232 VL - 14 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2007049/ DO - 10.1051/cocv:2007049 LA - en ID - COCV_2008__14_2_211_0 ER -
%0 Journal Article %A Steinhauer, Mark %A Málek, Josef %A Diening, Lars %T On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 211-232 %V 14 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv:2007049/ %R 10.1051/cocv:2007049 %G en %F COCV_2008__14_2_211_0
Steinhauer, Mark; Málek, Josef; Diening, Lars. On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 211-232. doi : 10.1051/cocv:2007049. https://www.numdam.org/articles/10.1051/cocv:2007049/
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