Geodesic
Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case $q=\frac{3d}{d+2}$
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 659-668.

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In this paper we consider weak solutions ${\bold u}: \Omega \rightarrow \Bbb R^d$ to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain $\Omega \subset \Bbb R^d$ ($d=2$ or $d=3$). For the critical case $q=\frac{3d}{d+2}$ we prove the higher integrability of $\nabla {\bold u}$ which forms the basis for applying the method of differences in order to get fractional differentiability of $\nabla {\bold u}$. From this we show the existence of second order weak derivatives of $u$.
Classification : 35B65, 35D10, 35D30, 35Q30, 35Q35, 76A05
Keywords: non-Newtonian fluids; weak solutions; interior regularity 
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     author = {Wolf, J\"org},
     title = {Interior regularity of weak solutions to the equations of a stationary motion of a {non-Newtonian} fluid with shear-dependent viscosity. {The} case $q=\frac{3d}{d+2}$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     number = {4},
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     zbl = {1199.35297},
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Wolf, Jörg. Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case $q=\frac{3d}{d+2}$. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 659-668. http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a8/