no. 1
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 
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     title = {On the equality between {Monge's} infimum and {Kantorovich's} minimum in optimal mass transportation},
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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

[1] L. Ambrosio, Lecture notes on optimal transport problems, in: Mathematical Aspects of Evolving Interfaces, Lecture Notes in Math., vol. 1812, Springer, 2003, pp. 1-52. | Zbl | MR

[2] L. Ambrosio, A. Pratelli, Existence and stability results in the L 1 theory of optimal transportation, in: Optimal Transportation and Applications, Lecture Notes in Math., vol. 1813, Springer, 2003, pp. 123-160. | Zbl | MR

[3] L. Caffarelli, M. Feldman, R.J. Mccann, Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs, J. Amer. Math. Soc. 15 (2002) 1-26. | Zbl | MR

[4] L.C. Evans, W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc. 137 (653) (1999). | Zbl

[5] W. Gangbo, The Monge mass transfer problem and its applications, Contemp. Math. 226 (1999) 79-104. | Zbl | MR

[6] L.V. Kantorovich, On the transfer of masses, Dokl. Akad. Nauk SSSR 37 (1942) 227-229.

[7] L.V. Kantorovich, 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] J.C. Oxtoby, Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24 (1970) 419-423. | Zbl | MR

[10] A. Pratelli, 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] S.T. Rachev, L. Rüschendorf, Mass Transportation Problems, Springer-Verlag, 1998.

[12] H.L. Royden, Real Analysis, second ed., Macmillan, 1968. | Zbl

[13] N.S. Trudinger, X.J. Wang, On the Monge mass transfer problem, Calc. Var. Partial Differential Equations 13 (2001) 19-31. | Zbl | MR

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