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arXiv · 1311.5868

Obstructions to regularity in the classical Monge problem

Maria Colombo·Emanuel Indrei
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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 the counterexample in \cite{LSW} to Lipschitz regularity of the monotone optimal map between smooth densities supported on convex domains.

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Maria Colombo, Emanuel Indrei. 2013-11-22. Obstructions to regularity in the classical Monge problem. https://arxiv.org/abs/1311.5868

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