@article{AIHPB_2007__43_1_1_0, author = {Pratelli, Aldo}, title = {On the equality between {Monge's} infimum and {Kantorovich's} minimum in optimal mass transportation}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1--13}, publisher = {Elsevier}, volume = {43}, number = {1}, year = {2007}, doi = {10.1016/j.anihpb.2005.12.001}, mrnumber = {2288266}, zbl = {1121.49036}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.12.001/} }
TY - JOUR AU - Pratelli, Aldo TI - On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2007 SP - 1 EP - 13 VL - 43 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2005.12.001/ DO - 10.1016/j.anihpb.2005.12.001 LA - en ID - AIHPB_2007__43_1_1_0 ER -
%0 Journal Article %A Pratelli, Aldo %T On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation %J Annales de l'I.H.P. Probabilités et statistiques %D 2007 %P 1-13 %V 43 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2005.12.001/ %R 10.1016/j.anihpb.2005.12.001 %G en %F AIHPB_2007__43_1_1_0
Pratelli, Aldo. On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 1, pp. 1-13. doi : 10.1016/j.anihpb.2005.12.001. http://www.numdam.org/articles/10.1016/j.anihpb.2005.12.001/
[1] Lecture notes on optimal transport problems, in: Mathematical Aspects of Evolving Interfaces, Lecture Notes in Math., vol. 1812, Springer, 2003, pp. 1-52. | MR | Zbl
,[2] Existence and stability results in the theory of optimal transportation, in: Optimal Transportation and Applications, Lecture Notes in Math., vol. 1813, Springer, 2003, pp. 123-160. | MR | Zbl
, ,[3] Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs, J. Amer. Math. Soc. 15 (2002) 1-26. | MR | Zbl
, , ,[4] Differential equations methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc. 137 (653) (1999). | Zbl
, ,[5] The Monge mass transfer problem and its applications, Contemp. Math. 226 (1999) 79-104. | MR | Zbl
,[6] On the transfer of masses, Dokl. Akad. Nauk SSSR 37 (1942) 227-229.
,[7] On a problem of Monge, Uspekhi Mat. Nauk 3 (1948) 225-226.
,[8] G. Monge, Memoire sur la Theorie des Déblais et des Remblais, Hist. de l'Acad. des Sciences de Paris, 1781.
[9] Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24 (1970) 419-423. | MR | Zbl
,[10] Existence of optimal transport maps and regularity of the transport density in mass transportation problems, Ph.D. Thesis, Scuola Normale Superiore, Pisa, Italy, 2003. Available on, http://cvgmt.sns.it/.
,[11] Mass Transportation Problems, Springer-Verlag, 1998.
, ,[12] Real Analysis, second ed., Macmillan, 1968. | Zbl
,[13] On the Monge mass transfer problem, Calc. Var. Partial Differential Equations 13 (2001) 19-31. | MR | Zbl
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