A characterization for solutions of the Monge-Kantorovich mass transport problem
Abbas Moameni
TL;DR
This paper introduces a measure-theoretic framework for analyzing the Monge-Kantorovich optimal mass transport problem, providing new insights into the support of optimal plans and conditions for their uniqueness.
Contribution
It offers a novel measure-theoretic approach combined with Kantorovich duality to characterize solutions and determine uniqueness in the mass transport problem.
Findings
Provided a criterion for the uniqueness of optimal plans.
Characterized the support of optimal plans for general cost functions.
Developed an effective tool for analyzing the mass transport problem.
Abstract
A measure theoretical approach is presented to study the Monge-Kantorovich optimal mass transport problem. This approach together with Kantorovich duality provide an effective tool to answer a long standing question about the support of optimal plans for the mass transport problem involving general cost functions. We also establish a criterion for the uniqueness.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations