A variational approach to regularity theory in optimal transportation | Zendy

Michaël Goldman | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A variational approach to regularity theory in optimal transportation

Author(s) -

Michaël Goldman

Publication year - 2019

Publication title -

séminaire laurent schwartz — edp et applications

Language(s) - English

Resource type - Journals

ISSN - 2266-0607

DOI - 10.5802/slsedp.132

Subject(s) - linearization , poisson's equation , mathematics , matching (statistics) , poisson distribution , identity (music) , mathematical economics , mathematical optimization , calculus (dental) , mathematical analysis , nonlinear system , physics , statistics , medicine , dentistry , quantum mechanics , acoustics

This paper describes recent results obtained in collaboration with M. Huesmann and F. Otto on the regularity of optimal transport maps. The main result is a quantitative version of the well-known fact that the linearization of the Monge-Amp{e}re equation around the identity is the Poisson equation. We present two applications of this result. The first one is a variational proof of the partial regularity theorem of Figalli and Kim and the second is the rigorous validation of some predictions made by Carraciolo and al. on the structure of the optimal transport maps in matching problems.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research