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Journal of Convex Analysis 31 (2024), No. 2, 603--618
Copyright Heldermann Verlag 2024

Existence and Uniqueness of Monge Minimizers for a Multi-Marginal Optimal Transport Problem with Intermolecular Interactions Cost

Augusto Gerolin
Dept. of Mathematics and Statistics, and: Dept. of Chemistry and Biomolecular Sciences, and: Nexus for Quantum Technologies, University of Ottawa, Canada

Mircea Petrache
Dept. of Mathematics, and: Inst. for Mathematical and Computational Engineering, Pontificia Universidad Católica, Santiago, Chile

Adolfo Vargas-Jiménez
Department of Mathematics and Statistics, University of Ottawa, Canada

We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we introduce such dissociation model, the corresponding optimal transport problem as well as show preliminary results on the existence and uniqueness of Monge solutions assuming absolute continuity of at least two of the marginals. Finally, we show that such marginal regularity conditions are necessary for the existence of an unique Monge solution.

Keywords: Multi-marginal optimal transport, density functional theory, dissociation energy.

MSC: 49-XX, 35-XX.

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