A1 Journal article (refereed)
On deterministic solutions for multi-marginal optimal transport with Coulomb cost (2022)

Bindini, U., De Pascale, L., & Kausamo, A. (2022). On deterministic solutions for multi-marginal optimal transport with Coulomb cost. Communications on Pure and Applied Analysis, 21(4), 1189-1208. https://doi.org/10.3934/cpaa.2022015

JYU authors or editors

Publication details

All authors or editors: Bindini, Ugo; De Pascale, Luigi; Kausamo, Anna

Journal or series: Communications on Pure and Applied Analysis

ISSN: 1534-0392

eISSN: 1553-5258

Publication year: 2022

Volume: 21

Issue number: 4

Pages range: 1189-1208

Publisher: American Institute of Mathematical Sciences (AIMS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.3934/cpaa.2022015

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/79667

Publication is parallel published: https://arxiv.org/abs/2011.05063

Abstract

In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane R2. 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 class of regular counterexamples to the optimality of this family of maps.

Keywords: calculus of variations; mathematical optimisation; density functional theory

Free keywords: multimarginal optimal transportation; Monge-Kantorovich problem; duality theory; Coulomb cost; Density Functional Theory.

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 1