Existence and Uniqueness of Monge Minimizers for a Multi-Marginal Optimal Transport Problem with Intermolecular Interactions Cost
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Date
2024
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Abstract
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.
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Keywords
Multi-marginal optimal transport, density functional theory, dissociation energy