Partial regularity for optimal transport maps
De Philippis, Guido1 ; Figalli, Alessio2
1 Scuola Normale Superiore p.za dei Cavalieri 7 56126 Pisa Italy
2 Department of Mathematics, The University of Texas at Austin 1 University Station C1200 78712 Austin TX USA
Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 81-112.

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.

DOI : 10.1007/s10240-014-0064-7
Mots clés : Riemannian Manifold, Partial Regularity, Optimal Transport, Optimal Transportation, Smooth Density
De Philippis, Guido 1 ; Figalli, Alessio 2

1 Scuola Normale Superiore p.za dei Cavalieri 7 56126 Pisa Italy
2 Department of Mathematics, The University of Texas at Austin 1 University Station C1200 78712 Austin TX USA 
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De Philippis, Guido; Figalli, Alessio. Partial regularity for optimal transport maps. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 81-112. doi : 10.1007/s10240-014-0064-7. http://www.numdam.org/articles/10.1007/s10240-014-0064-7/

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