Adv. Math. Econ. Volume 1, pp.99-113 (1999)

Analysis of the asymptotic distance between oscillating functions and their weak limit in L²

Michel Valadier
Département de Mathématiques - case 051, Université Montpellier II, place Eugène Bataillon, 34095 Montpellier Cedex 5, France

Young measures theory is applied to the understanding of weak convergence without strong convergence in L² spaces. The two-scale Young measures permit also to analyse, when it happens, a "modulated periodical" behavior and, in the general case, to get a kind of orthogonal decomposition. Some new examples are discussed.

Weak convergence, oscillations, asymptotic behavior, Young measures, two-scale convergence