
Journal of Convex Analysis 31 (2024), No. 2, 603618 Copyright Heldermann Verlag 2024 Existence and Uniqueness of Monge Minimizers for a MultiMarginal 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 agerolin@uottawa.ca Mircea Petrache Dept. of Mathematics, and: Inst. for Mathematical and Computational Engineering, Pontificia Universidad Católica, Santiago, Chile mpetrache@mat.puc.cl Adolfo VargasJiménez Department of Mathematics and Statistics, University of Ottawa, Canada We investigate a new multimarginal 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: Multimarginal optimal transport, density functional theory, dissociation energy. MSC: 49XX, 35XX. [ Fulltextpdf (153 KB)] for subscribers only. 