On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 2, p. 211-232

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 : https://doi.org/10.1051/cocv:2007049
Classification:  35J55,  35J65,  35J70,  35Q35,  76D99
Keywords: Lipschitz truncation of W 0 1,p /W 0 1,p(·) -functions, existence, weak solution, incompressible fluid, power-law fluid, electro-rheological fluid
@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},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {2},
     year = {2008},
     pages = {211-232},
     doi = {10.1051/cocv:2007049},
     zbl = {1143.35037},
     mrnumber = {2394508},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 14 (2008) no. 2, pp. 211-232. doi : 10.1051/cocv:2007049. http://www.numdam.org/item/COCV_2008__14_2_211_0/

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