Partial Regularity for optimal transport maps

2012/09/25 by De Philippis, Guido, Figalli, Alessio · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.5640

Abstract

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.

Cited by

• Partial regularity of optimal transport with Coulomb cost
• A quantitative stability result for regularity of optimal transport on compact manifolds

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