Geodesic
Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs
Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 350-368

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DOI

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.
DOI : 10.4153/CJM-2014-011-x
Mots-clés : 49Q20, 49K30, Monge–Kantorovich problem, optimal transport problem, cyclical monotonicity 
Colombo, Maria; Pascale, Luigi De; Marino, Simone Di. Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs. Canadian journal of mathematics, Tome 67 (2015) no. 2, pp. 350-368. doi: 10.4153/CJM-2014-011-x
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     author = {Colombo, Maria and Pascale, Luigi De and Marino, Simone Di},
     title = {Multimarginal {Optimal} {Transport} {Maps} for {One{\textendash}dimensional} {Repulsive} {Costs}},
     journal = {Canadian journal of mathematics},
     pages = {350--368},
     year = {2015},
     volume = {67},
     number = {2},
     doi = {10.4153/CJM-2014-011-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-011-x/}
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