The JKO scheme for Tonelli Lagrangians

par Alexander Paschal

mercredi 17 juin 2026, 10:30 → 12:30 Europe/Paris

112 (Braconnier)

We discuss Tonelli Lagrangians, which are classical objects in the calculus of variations. Of particular interest are the properties of these Lagrangians (for example, local semi-concavity and the twist condition) that are used in the work of Fathi-Figalli on optimal transport for so-called Lagrangian costs on non-compact manifolds. We then move to the work of Figalli-Gangbo-Yolcu, which extends De Giorgi's interpolation method to prove the convergence of the JKO scheme for these general cost functions which may not induce a metric. If time permits, we will also discuss possible generalizations of their work.