Mathematical Research Letters

Volume 21 (2014)

Number 4

Obstructions to regularity in the classical Monge problem

Pages: 697 – 712



Maria Colombo (Scuola Normale Superiore, Pisa, Italy)

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


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.

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