Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Figalli

Partial regularity results in optimal transportation

created by dephilipp on 23 Feb 2014
modified on 18 Oct 2014


Springer INdAM series

Inserted: 23 feb 2014
Last Updated: 18 oct 2014

Year: 2014

Survey Paper


This note describes some recent results on the regularity of optimal transport maps. As we shall see, in general optimal maps are not globally smooth, but they are so outside a ``singular set'' of measure zero.