An explicit solution for a multimarginal mass transportation problem
arXiv:1809.08554 · doi:10.1137/18M122707X
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).
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