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.
Key Words:
Weak convergence, oscillations, asymptotic behavior, Young measures, two-scale convergence