Mathematical Research Letters

Volume 21 (2014)

Number 4

Obstructions to regularity in the classical Monge problem

Pages: 697 – 712

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n4.a6

Authors

Maria Colombo (Scuola Normale Superiore, Pisa, Italy)

Emanuel Indrei (Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Abstract

We provide counter-examples 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 the counter-example in [10] to Lipschitz regularity of the monotone optimal map between smooth densities supported on convex domains.

Full Text (PDF format)