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Application of Young measures to uniformly integrable sequences in a separable Banach space. (Application des mesures de Young aux suites uniformément integrables dans un Banach séparable.) (French) Zbl 0742.49010
The main results of the paper extend to a separable Banach space \(E\) well-known theorems of functional analysis and the calculus of variations. More precisely, the author proves the weak-compactness of a sequence \((u_ n)_ n\) of uniformly integrable functions in \(L^ 1(\Omega,\mu;E)\) and a lower semicontinuity result for integral functionals of the type \[ I[u,v]=\int_ \Omega \psi(\omega,u(\omega),v(\omega))d\mu \] with respect to the convergence in measure of a sequence \((u_ n)_ n\) of measurable functions and the weak convergence of a sequence \((v_ n)_ n\) in \(L^ 1(\Omega,\mu;E)\). The technique used makes use of the theory of Young measures [see also the author in: “Methods of nonconvex analysis”, Lect. Notes Math. 1446, 152-188 (1990; Zbl 0738.28004)].
Reviewer: C.Vinti (Perugia)

49J45 Methods involving semicontinuity and convergence; relaxation