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Search: MSC category 49K30 ( Optimal solutions belonging to restricted classes )

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1. CJM Online first

Jiang, Yin
Absolute continuity of Wasserstein barycenters over Alexandrov spaces
In this paper, we prove that, on a compact, $n$-dimensional Alexandrov space with curvature $\geqslant -1$, the Wasserstein barycenter of Borel probability measures $\mu_1,...,\mu_m$ is absolutely continuous with respect to the $n$-dimensional Hausdorff measure if one of them is.

Keywords:Alexandrov space, Wasserstein barycenter, multi-marginal optimal transport
Categories:51K05, 49K30

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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