Contents Online
Mathematical Research Letters
Volume 21 (2014)
Number 4
Obstructions to regularity in the classical Monge problem
Pages: 697 – 712
DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n4.a6
Authors
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.
Accepted 19 March 2014
Published 27 October 2014