Homogenization of Dirichlet and Neumann problems with gradient constraints

A homogenization theorem is established for the problem of minimization of an integral functional of the Calculus of Variation whose integrand f (y; z) takes values in [0;+infinity] : The unboundedness of the integrand can be interpreted as a rapidly oscillating constraint on the gradient of the admissible functions. The main assumptions on f (y; z) will be convexity and uniform p coerciveness, 1 < p < +infinity; in the z variable. Convergence results are proved for the Dirichlet and for the Neumann problem in both the scalar and the vectorial case.