Homogenization of problems in $^\infty$

We study the homogenization of functionals of the form

These functionals are related to a model of dielectric

breackdown and can be used as a variational approximation of

power-law energies. We compute optimal bounds in the case of

the mixtures of two materials, which exhibit a different

structure from the integral case.

We prove a homogenization theorem in a general context and compare it

with the corresponding result for the integral case.