Work

An Explicit Solution for a Multimarginal Mass Transportation Problem

Year: 2020

Type: article

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 a nonconstant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique (up to addition of constants).

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/18m122707x

Authors: Nikita A. Gladkov, Alexander P. Zimin

Institution: National Research University Higher School of Economics

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2890443840

FWCI: 1.443

Cites: 17

Cited by: 7

Related to: 20