Abstract

Given a bounded sequence (uₙ) in L¹ (Ω, µ;Rd\mathbb{R}^d), we describe the weak limits in the sense of measures of f(x, uₙ) µ for a class of continuous integrands with linear growth at infinity. The defect of uniform integrability of the sequence f(x, uₙ) is described by a measure m and a family of probability measures on Sd−1S^{d-1} whereas the classical Young measure is associated with the biting limits in the sense of Chacon’s lemma. Some consequences of this new approach are given in Calculus of Variations.

Author information

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J.J. Alibert

Laboratoire ANLA, UFR Science, Université de Toulon et du Var, BP 132, 83957 La Garde Cedex, France.

G. Bouchitté

Laboratoire ANLA, UFR Science, Université de Toulon et du Var, BP 132, 83957 La Garde Cedex, France.

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Suggested citation

J. J. Alibert, G. Bouchitté. “Non-Uniform Integrability and Generalized Young Measures.” Journal of Convex Analysis 4 (1997), No. 1, 129–147. https://doi.org/10.68381/jca04006

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Published by Heldermann Verlag, 1997. Rights now held by Banach Press LLC.