We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in and a corresponding example for a .
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 (2003) 1064–1083]. We also establish new existence results to a class of incompressible electro-rheological fluids.
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