H convergence for quasi-linear elliptic equations with quadratic growth

We consider in this paper the limit behavior of the solutions u^e{open} of the problem {Mathematical expression} where H^e{open} has quadratic growth in Du^e{open} and a^e{open}(x) is a family of matrices satisfying the general assumptions of abstract homogenization. We also consider the problem {Mathematical expression} where G^e{open} has quadratic growth in Du^e{open} and satisfies G^e{open}(x, s, ξ)s ≥ 0. Note that in this last model u^e{open} is in general unbounded, which gives extra difficulties for the homogenization process. In both cases we pass to the limit and obtain an homogenized equation having the same structure. © 1992 Springer-Verlag New York Inc.