Homogenization of Quasiconvex Integrals via the Periodic Unfolding Method

Abstract

The homogenization problem in the general case of quasiconvex integral energies with polynomial growth, defined on vector-valued configurations, was studied by the $\G$-convergence methods in [A. Braides, Rend. Accad. Naz. Sci. XL Mem. Mat. (5), 9 (1985), pp. 313-321] and [S. Müller, Arch. Rational Mech. Anal., 99 (1987), pp. 189-212]. This paper presents a new proof by means of the periodic unfolding method introduced in [D. Cioranescu, A. Damlamian, and G. Griso, C. R. Math. Acad. Sci. Paris, 335 (2002), pp. 99-104]. It is an elementary proof since it reduces the homogenization process to a weak convergence problem in an $L^p$-type space.