Geodesic
Remarks on Γ-Convergence and the Monge-Kantorovich Mass Transfer Problem
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 407-415
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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.
Classification : 49J45, 46N10
Mots-clés : Young measures, relaxed formulation, joint measure, marginals 
@article{JCA_2005_12_2_JCA_2005_12_2_a10,
     author = {P. Pedregal},
     title = {Remarks on {\ensuremath{\Gamma}-Convergence} and the {Monge-Kantorovich} {Mass} {Transfer} {Problem}},
     journal = {Journal of convex analysis},
     pages = {407--415},
     year = {2005},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a10/}
}
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P. Pedregal. Remarks on Γ-Convergence and the Monge-Kantorovich Mass Transfer Problem. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 407-415. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a10/