REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS

In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo 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.