Accepted Paper
Inserted: 1 dec 2013
Last Updated: 23 jul 2014
Journal: Math. Res. Lett.
Year: 2014
Abstract:
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.
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