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Search: MSC category 49Q20 ( Variational problems in a geometric measure-theoretic setting )

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1. CJM Online first

Cordero-Erausquin, Dario
Transport inequalities for log-concave measures, quantitative forms and applications
We review some simple techniques based on monotone mass transport that allow us to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these inequalities, with application to the Brascamp-Lieb variance inequality.

Keywords:log-concave measures, transport inequality, Brascamp-Lieb inequality, quantitative inequalities
Categories:52A40, 60E15, 49Q20

2. CJM 2014 (vol 67 pp. 350)

Colombo, Maria; De Pascale, Luigi; Di Marino, Simone
Multimarginal Optimal Transport Maps for One-dimensional Repulsive Costs
We study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.

Keywords:Monge-Kantorovich problem,optimal transport problem, cyclical monotonicity
Categories:49Q20, 49K30

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