Abstract
It is considered a function and w in the Muckenhoupt class A P , such that for every is almost periodic in the sense of Besicovitch and for every is convex. Then it is introduced a convex function , explicitly deduced f by such that for every bounded open set ω with Lipschitz boundary ψ and in L ∞(ω) the solutions of the problems min converge, up to subsequences, in L 1(ω) to solutions of min and the convergence of the whole sequence of the minimum values holds.