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.-truncations of W 1,p 0 -functions that are useful from the point of view of the existence theory concerning nonlinear PDE's. We illustrate the potential of this tool by establishing the weak stability for the system of p-Laplace equations with very general right-hand sides.Then, in Section 3 we exploit Lipschitz truncations in the analysis of steady flows of generalized power-law fluids. In this case we reprove in a simplified way the existence results established in [18].
The p-Laplace equation is considered for p > 2 on a n-dimensional convex polyhedral domain under a Dirichlet boundary value condition. Global regularity of weak solutions in weighted Sobolev spaces and in fractional order Nikolskij and Sobolev spaces are proven.
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