Reiterated homogenization of degenerate nonlinear elliptic equations

The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h(2)x, Du(h))) = f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied. It is proved that u(h) converges weakly in W-0(1,1) (Omega) to the unique solution of a limit problem as h --> infinity. Moreover, explicit expressions for the limit problem are obtained.