Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

La multi-application médianes conditionnelles

Sans résumé Remerciements. L'auteur remercie le rapporteur pour l'amélioration du théorème qu'il a suggérée.     

Méthodes de troncature appliqués à des problèmes de convergence faible ou forte dans L1

Sans résumé     

Young measures, weak and strong convergence and the Visintin-Balder Theorem

This paper is concerned with sequences inL ¹ which converge weakly. Young's measures theory permits us to give sufficient conditions insuring the strong convergence and to understand the behaviour of the sequences which do not converge strongly.     

On conditional expectation of random sets

Summary Let be a random set with values in closed convex non empty subsets of the dual of a separable Fréchet space. Then its conditional expectation with respect to a sub-tribe is proved to exist and is related to regulat conditional probability.     

Théorème de Hoffmann-Jorgensen et application aux amarts multivoques

Annali di Matematica Pura ed Applicata (1923 -) - On présente ici des versions univoques et multivoques d'un résultat de Hoffmann-Jorgensen ([10]). Ces résultats permettent...     

Evolution equations governed by the sweeping process

This paper is concerned with variants of the sweeping process introduced by J.J. Moreau in 1971. In Section 4, perturbations of the sweeping process are studied. The equation has the formX(t) -N _C(t) (X(t)) +F(t, X(t)). The dimension is finite andF is a bounded closed convex valued multifunction. WhenC(t) is the complementary of a convex set,F is globally measurable andF(t, ·) is upper semicontinuous, existence is proved (Th. 4.1). The Lipschitz constants of the solutions receive particular attention. This point is also examined for the perturbed version of the classical convex sweeping process in Th. 4.1. In Sections 5 and 6, a second-order sweeping process is considered:X (t) -N _C(X(t)) (X(t)). HereC is a bounded Lipschitzean closed convex valued multifunction defined on an open subset of a Hilbert space. Existence is proved whenC is dissipative (Th. 5.1) or when allC(x) are contained in a compact setK (Th. 5.2). In Section 6, the second-order sweeping process is solved in finite dimension whenC is continuous.