In this talk, I shall present a relaxation formula and duality theory for the multi-marginal Coulomb cost that appears in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which are sub-probabilities. I will introduce the duality framework associated to this kind of cost, and apply it to a model type of minimization problems for which it appears a mass quantization effect for the optimal solutions. All the necessary material on optimal transport will be introduced during the talk.

This is a joint work with G. Bouchitté (Univ. Toulon), G. Buttazzo (Univ. Pisa) and L. De Pascale (Univ. Firenze).

Zoom meeting: Link