Periodic homogenization for convex functionals using Mosco convergence

We study the relationship between the Mosco convergence of a sequence of convex proper lower semicontinuous functionals, defined on a reflexive Banach space, and the convergence of their subdifferentiels as maximal monotone graphs. We then apply these results together with the unfolding method (see Cioranescu et al. in C R Math Acad Sci Paris 355:99–104, 2002) to study the homogenization of equations of the form \({-\textrm{ div }d_\varepsilon=f }\), with \({(\nabla u_\varepsilon(x),d_\varepsilon(x)) \in \partial \varphi_\varepsilon(x)}\) where \({\varphi_\varepsilon (x,.)}\) is a Carathéodory convex function with suitable growth and coercivity conditions.