The existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition

In this paper, we show the existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition under the condition p(x)>2nn+2, n=2,3. In particular, we improve a priori estimate for weak solutions to the problem with minp(x)<2, which is an improvement even for constant p.