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

Steinhauer, Mark; Málek, Josef; Diening, Lars

ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 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.

Classification : 35J55, 35J65, 35J70, 35Q35, 76D99
Mots clés : 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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