A differential approach to the multi-marginal Schrödinger system

Guillaume Carlier (1) , Maxime Laborde (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics and Statistics [Montréal]

We develop an elementary and self-contained differential approach, in an L ∞ setting, for well-posedness (existence, uniqueness and smooth dependence with respect to the data) for the multi-marginal Schrödinger system which arises in the entropic regularization of optimal transport problems.

Mots clés: Multi-marginal Schrödinger system; local and global inverse function theorems; entropy minimization MS Classification: 45G15; 49K40

Domaines: Analyse fonctionnelle [math.FA]; Optimisation et contrôle [math.OC]

Guillaume Carlier, Maxime Laborde. A differential approach to the multi-marginal Schrödinger system. 2018. ⟨hal-01918578v1⟩