Regularity of the Monge-Ampère equation via variational arguments

par Aymeric Baradat

mercredi 27 nov. 2024, 10:00 → 11:30 Europe/Paris

Fokko du Cloux (Braconnier)

The aim of this presentation is to discuss a series of papers by Goldman, Huesmann, and Otto, which offer a variational proof of regularity for the Monge-Ampère equation. The key argument in these works is a quantitative statement based on the observation that the linearization of the Monge-Ampère equation corresponds to the Poisson equation. In plain words, when the transport cost is small and the targeted measures are close to constant, then the transport map is extremely close to the gradient of a harmonic function. I will prove this approximation result in detail, and highlight its application in establishing regularity via Campanato iterations.