Nonlinear variational inequalities with bilateral constraints coinciding on a set of positive measure

We consider variational inequalities with invertible operators in divergence form and constraint set a.e. in where is a nonempty bounded open set in , , and are measurable functions. Under the assumptions that the operators G-converge to an invertible operator , , and there exist functions such that a.e. in and we establish the weak convergence in of the solutions of the specified variational inequalities to the solution of a similar variational inequality with the operator and the constraint set The fundamental difference between the considered case and the previously studied case, where is that, in general, the functionals do not converge to even weakly in and the energy integrals do not converge to .