On deterministic solutions for multi-marginal optimal transport with Coulomb cost
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
American Institute of Mathematical Sciences (AIMS)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202202071421Use this for linking
Review status
Peer reviewed
ISSN
1534-0392
DOI
https://doi.org/10.3934/cpaa.2022015
Language
English
Published in
Communications on Pure and Applied Analysis
Citation
- 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
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Additional information about funding
The second and third authors are partially supported by the project:Alcuni problemi di trasporto ottimo ed applicazioni of GNAMPA-INDAM, the second author is partially supported by Fondi di Ateneo of the University of Firenze, the third author was partially supported by the project Contemporary topics on multi-marginal optimal mass transportation, funded by the Finnish Postdoctoral Pool (Suomen Kulttuurisäätiö).
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