Reiterated homogenization of nonlinear monotone operators

In this paper, the authors study reiterated homogenization of nonlinear equations of the form -div(a(x,x/epsilon ,x/epsilon (2), Du(epsilon))) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that u(epsilon) converges weakly in W-1,W-p (Ohm) (and even in some multiscale sense), as epsilon --> 0 to the solution u(0) of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.