Work

On Uniqueness of an Optimal Solution to the Kantorovich Problem With Density Constraints

Year: 2024

Type: article

Abstract: We study optimal transportation problems with constraints on densities of transport plans. We obtain a sharp condition for the uniqueness of an optimal solution to the Kantorovich problem with density constraints, namely that the Borel measurable cost function $h(x, y)$ satisfies the following non-degeneracy condition: $h(x, y)$ cannot be expressed as a sum of functions $u(x) + v(y)$ on a set of positive measure.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae178

Author: Svetlana N Popova

Institutions: National Research University Higher School of Economics, Lomonosov Moscow State University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Russian Science Foundation

Award: G1091941066