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Journal of Convex Analysis 12 (2005), No. 2, 407--415
Copyright Heldermann Verlag 2005

Remarks on Γ-Convergence and the Monge-Kantorovich Mass Transfer Problem

Pablo Pedregal
ETSI Industriales, Universidad de Castilla - La Mancha, 13071 Ciudad Real, Spain

By looking at the Γ-convergence of some easy functionals in terms of underlying Young measures, we emphasize the connection of this issue with the Monge-Kantorovich mass transfer problem. After exploring this relationship, we study a typical example in periodic homogenization to realize the difference between the Monge-Kantorovich problem and the usual cell problem. We also state a version of the Monge-Kantorovich problem for gradients.

Keywords: Young measures, relaxed formulation, joint measure, marginals.

MSC: 49J45; 46N10

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