Calculus of Variations and Geometric Measure Theory

M. Colombo - E. Indrei

Obstructions to regularity in the classical Monge problem

created by colombom on 01 Dec 2013
modified on 23 Jul 2014


Accepted Paper

Inserted: 1 dec 2013
Last Updated: 23 jul 2014

Journal: Math. Res. Lett.
Year: 2014


We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of a recent counterexample by Li, Santambrogio, and Wang to Lipschitz regularity of the monotone optimal map between smooth densities supported on convex domains.