Geodesic
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

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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. Anal 34 (2003) 1064-1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.

DOI : 10.1051/cocv:2007049
Classification : 35J55, 35J65, 35J70, 35Q35, 76D99
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 
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     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 = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007049/}
}
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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

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