Calculus of Variations and Geometric Measure Theory

U. Bindini - L. De Pascale - A. Kausamo

On Seidl-type maps for multi-marginal optimal transport with Coulomb cost

created by bindini on 03 Aug 2021


Submitted Paper

Inserted: 3 aug 2021
Last Updated: 3 aug 2021

Year: 2020

ArXiv: 2011.05063 PDF


In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane ${\mathbb R}^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite family of regular counterexamples to the optimality of Seidl-type maps.