Geodesic
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 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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
Keywords: 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 
@article{PMIHES_2015__121__81_0,
     author = {De Philippis, Guido and Figalli, Alessio},
     title = {Partial regularity for optimal transport maps},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {81--112},
     year = {2015},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {121},
     doi = {10.1007/s10240-014-0064-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0064-7/}
}
TY  - JOUR
AU  - De Philippis, Guido
AU  - Figalli, Alessio
TI  - Partial regularity for optimal transport maps
JO  - Publications Mathématiques de l'IHÉS
PY  - 2015
SP  - 81
EP  - 112
VL  - 121
PB  - Springer Berlin Heidelberg
PP  - Berlin/Heidelberg
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0064-7/
DO  - 10.1007/s10240-014-0064-7
LA  - en
ID  - PMIHES_2015__121__81_0
ER  - 
%0 Journal Article
%A De Philippis, Guido
%A Figalli, Alessio
%T Partial regularity for optimal transport maps
%J Publications Mathématiques de l'IHÉS
%D 2015
%P 81-112
%V 121
%I Springer Berlin Heidelberg
%C Berlin/Heidelberg
%U http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0064-7/
%R 10.1007/s10240-014-0064-7
%G en
%F PMIHES_2015__121__81_0
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

Cité par Sources :