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

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.