Calculus of Variations and Geometric Measure Theory

F. Santambrogio

Introduction to Optimal Transport Theory

created by santambro on 04 Mar 2010
modified on 27 Nov 2014


Published Paper

Inserted: 4 mar 2010
Last Updated: 27 nov 2014

Journal: chapter in "Optimal Transportation, theory and applications", London Math. Soc.
Year: 2014

Proceedings of the summer school "Optimal transport: Theory and applications"


These very short lecture notes do not obviously want to be an exhaustive presentation of the topic, but only a short list of results, concepts and ideas which are useful when dealing for the first time with the theory of Optimal Transport. The style that was chosen when preparing them, in view of their use during the Summer School, was highly informal and this revised version respects the same style.

Keywords: displacement convexity, Monge problem, Wasserstein distance, regularity, continuity equation, Kantorovich problem, duality, curves of measures