An explicit solution for a multimarginal mass transportation problem
Abstract
We construct an explicit solution for the multimarginal transportation problem on the unit cube with the cost function 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).
Keywords
Cite
@article{arxiv.1809.08554,
title = {An explicit solution for a multimarginal mass transportation problem},
author = {Nikita A. Gladkov and Alexander P. Zimin},
journal= {arXiv preprint arXiv:1809.08554},
year = {2023}
}
Comments
31 pages, 4 figures. The paper was completely rewritten. Heuristic considerations to find a solution of the primal problem added. Algorithm to find the primal problem solution numerically added (arbitrary marginals). The construction was generalized for a C(ln x + ln y + ln z), C is convex. Measure on the triangle was found with the support singular with respect to the Lebesgue measure