REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS
J. L. Lions, Dag Lukkassen, Lars‐Erik Persson, Peter Wall · Chinese Annals of Mathematics Series B · 2001
In this paper, the authors study reiterated homogenization of nonlinear equations of the form -div(a(x, x/ε, x/ε2,Duε)) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that uε converges weakly in W1,p(Ω) (and even in some multiscale sense), as ε → 0 to the solution u0 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