Homogenization in weighted Sobolev spaces
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.
homogenization of degenerate functionals
scientific article; zbMATH DE number 3983975