Partial regularity for optimal transport maps

By Guido De Philippis, Alessio Figalli. Publications mathématiques (Bures-sur-Yvette), 2012

67 citations recorded by the source corpus.

We prove that, for general cost functions on Rn, or for the cost d2/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f73605fa20da1d2fcc5c79b032435a4e7a0d9fb

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In Applied Mathematics

1. Guido De Philippis
2. Alessio Figalli
3. Filippo Santambrogio
4. Max Fathi
5. Luigi Ambrosio
6. Nicola Gigli
7. Dario Trevisan
8. Connor Mooney

In Mathematical Physics

1. Guido De Philippis
2. Alessio Figalli
3. Luigi Ambrosio

Citations in the corpus

• The Monge–Ampère equation and its link to optimal transportation (2013, background): “tive sectional curvature we have that the MTW condition fails at every point. This fact could make one suspect that the transport map could be extremely irregular. However, as shown by the authors in [40], this negative picture cannot happen: Theorem 4.11. Let X;Y ˆRn be two bounded open sets, and l”