REITERATED HOMOGENIZATION OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS

The authors study homogenization of some nonlinear partial differential equations of the form -div (a (hx, h²x, 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 to the unique solution of a limit problem as h → ∞. Moreover, explicit expressions for the limit problem are obtained.