Correctors for some nonlinear monotone operators

In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/epsilon h,Du(h))) = f(h) on Omega with Dirichlet boundary conditions. Here the sequence (epsilon (h)) tends to 0 a s h --> infinity and the map a(x,y,xi) is periodic in y, monotone in xi and satis es suitable continuity conditions. We prove that u(h) --> u weakly i n W-0(1,p) (Omega) as h --> infinity, where u is the solution of a homogeni zed problem of the form-div(b(x,Du)) = f on Omega. We also derive an explic it expression for the homogenized operator and prove some corrector results , i.e. we find (P-h) such that Du(h) - P-h (Du) --> 0 in L-p (Omega, R-n).