Homogeneization is the mathematical study of problems with parameters oscillating on a small scale with respect to the size of the problem, in order e.g. to obtain effective models for composite materials. In the case of periodic homogeneization, Cioranescu, Damlamian and Griso have developed the powerful unfolding method.
Nicolas Meunier and I have applied this method to nonlinear elliptic problem. In collaboration with Alain Damlamian we have extended the results to the case of maximal monotone graphs and subdifferentials of convex functions.
Alain Damlamian, Nicolas Meunier and Jean Van Schaftingen, Periodic homogenization for convex functionals using Mosco convergence, Ricerche Mat. 57 (2008), no. 2, 209–249.
doi:10.1007/s11587-008-0038-5 SharedIt DIAL:69506
Alain Damlamian, Nicolas Meunier and Jean Van Schaftingen, Periodic homogenization of monotone multivalued operators, Nonlinear Anal. 67 (2007), no. 12, 3217–3239.
doi:10.1016/j.na.2006.10.007 DIAL:37277 preprint
Nicolas Meunier and Jean Van Schaftingen, Periodic reiterated homogenization for elliptic functions, J. Math. Pures Appl. (9) 84 (2005), no. 12, 1716–1743.
doi:10.1016/j.matpur.2005.08.003 MR:2180388 DIAL:38986
Nicolas Meunier and Jean Van Schaftingen, Reiterated homogenization for elliptic operators, C. R. Math. Acad. Sci. Paris 340 (2005), no. 3, 209–214.
doi:10.1016/j.crma.2004.10.026 MR:2123030 DIAL:39532 preprint
