Relaxed multi-marginal costs in optimal transport and quantization effects

Jeudi 21 novembre 14:00-15:00 - Thierry Champion - Université de Toulon

Résumé : In this talk, we 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.
We first characterize the N-marginals relaxed cost in terms of a stratification formula which takes into account all interactions of k particles, with k lower than N. We then develop a duality framework and deduce primal-dual necessary and sufficient optimality conditions. Finaly we apply these results to a minimization problem involving a given continuous potential and we give evidence of a mass quantization effect for the optimal solutions.
This is a joint work with G. Bouchitté (Univ. Toulon), G. Buttazzo (Univ. Pisa) and L. De Pascale (Univ. Firenze)

Lieu : IMO, Salle 3L8

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