An external dual charge approach to the multimarginal optimal transport with Coulomb cost (Q6612248)

The paper deals with the multimarginal optimal transport problem with Coulomb cost, widely known in physics as the Strictly-Correlated Electrons functional. It establishes that the dual Kantorovich potential corresponds to an electrostatic potential generated by an external charge density, referred to as the dual charge. The author explores the properties of this dual charge, providing deeper insight into the structure of the dual potential. Additionally, the paper presents a discretization framework for the potential, demonstrating its application in both one-dimensional and three-dimensional spatial settings, thus connecting theoretical analysis with computational implementation.