We study the anisotropic boundary-value problem
−∑i=1N∂∂xiai(x,∂∂xiu)=fin Ω,u=0on ∂Ω,

where Ω is a smooth bounded domain in ℝN (N≥3). We obtain the existence and uniqueness of a weak energy solution for f∈L∞(Ω), and the existence of weak energy solution for general data f dependent on u.

ev spaces; weak energy solution; variable exponents; electrorheological fluids