Calculus of Variations and Geometric Measure Theory

S. Di Marino - A. Gerolin - L. Nenna

Optimal transportation theory for repulsive costs

created by dimarino on 23 Jun 2015
modified by nenna on 16 Jan 2018


Published Paper

Inserted: 23 jun 2015
Last Updated: 16 jan 2018

Journal: Topological Optimization and Optimal Transport In the Applied Sciences
Year: 2017

ArXiv: 1506.04565 PDF


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.