| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 56 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2024017 | |
| Published online | 07 August 2024 | |
An External Dual Charge Approach to the Multimarginal Optimal Transport with Coulomb Cost
CEREMADE, Université Paris-Dauphine, PSL Research University, Place de Lattre de Tassigny, 75016 Paris, France
* Corresponding author: lelotte@ceremade.dauphine.fr
Received:
11
September
2023
Accepted:
7
March
2024
In this paper, we study the multimarginal optimal transport with Coulomb cost, also known in the physics literature as the Strictly-Correlated Electrons functional. We prove that the dual Kantorovich potential is an electrostatic potential induced by an external charge density, which we call the dual charge. We study its properties and use it to discretize the potential in one and three space dimensions.
Mathematics Subject Classification: 49Q22 / 49N15 / 49N60 / 49S05
Key words: Multimarginal Optimal Transport / Strictly Correlated Electrons
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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