Solvability of nonlinear anisotropic elliptic unilateral problems with variable exponent

Abstract

In this paper, we study in the anisotropic Sobolev spaces with variable exponent W₀^{1, p(.)}(Ω), the existence result of unilateral problem associated to the equations of the form,

-∑_i=1^N ∂_i a_i(x, u, ∇ u) = g,

where the right hand side f belongs to L¹(Ω).