A variational approach to regularity theory in optimal transportation
Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 13, 14 p.

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-Ampère 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.

Publié le :
DOI : https://doi.org/10.5802/slsedp.132
@article{SLSEDP_2018-2019____A13_0,
author = {Goldman, Michael},
title = {A variational approach to regularity theory in optimal~transportation},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:13},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2018-2019},
doi = {10.5802/slsedp.132},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.132/}
}
Goldman, Michael. A variational approach to regularity theory in optimal transportation. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 13, 14 p. doi : 10.5802/slsedp.132. http://www.numdam.org/articles/10.5802/slsedp.132/

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