Homogenization in weighted Sobolev spaces (Q1086494)

We study, in the framework of weighted Sobolev spaces, the homogenization of degenerate functionals of the type \(\int \sum_{ij}a_{ij}(x/\epsilon)w(x)D_ iuD_ judx\), with \(a_{ij}\) periodic functions. We give a representation formula for the homogenized functional and, as in the uniformly elliptic case, we prove the convergence of the momenta to the momentum of the limit.