Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case
Jörg Wolf (2007)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we consider weak solutions to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain ( or ). For the critical case we prove the higher integrability of which forms the basis for applying the method of differences in order to get fractional differentiability of . From this we show the existence of second order weak derivatives of .