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arXiv · 1809.08554

An explicit solution for a multimarginal mass transportation problem

Nikita A. Gladkov·Alexander P. Zimin
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Abstract

We construct an explicit solution for the multimarginal transportation problem on the unit cube $[0,1]^3$ with the cost function $xyz$ and one-dimensional uniform projections. We show that the primal problem is concentrated on a set with non-constant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique (up to addition of constants).

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Nikita A. Gladkov, Alexander P. Zimin. 2018-09-23. An explicit solution for a multimarginal mass transportation problem. https://doi.org/10.1137/18m122707x

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