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Optimal transportation theory with repulsive costs

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Abstract

This survey intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions. We introduce some aspects of the Density Functional Theory (DFT) from a mathematical viewpoint, and revisit the theory of optimal transport from its perspective. Moreover, in the last three sections, we describe some recent and new theoretical and numerical results obtained for the Coulomb cost, the repulsive harmonic cost and the determinant.
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Dates and versions

hal-01163737 , version 1 (15-06-2015)
hal-01163737 , version 2 (01-12-2015)

Identifiers

  • HAL Id : hal-01163737 , version 2

Cite

Simone Di Marino, Augusto Gerolin, Luca Nenna. Optimal transportation theory with repulsive costs. 2015. ⟨hal-01163737v2⟩
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