On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation

Aldo Pratelli

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 1, page 1-13
  • ISSN: 0246-0203

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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 43.1 (2007): 1-13. <http://eudml.org/doc/77922>.

@article{Pratelli2007,
author = {Pratelli, Aldo},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Monge problem; optimal transport},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Elsevier},
title = {On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation},
url = {http://eudml.org/doc/77922},
volume = {43},
year = {2007},
}

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
PB - Elsevier
VL - 43
IS - 1
SP - 1
EP - 13
LA - eng
KW - Monge problem; optimal transport
UR - http://eudml.org/doc/77922
ER -

References

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  1. [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. Zbl1047.35001MR2011032
  2. [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. Zbl1065.49026MR2006307
  3. [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. Zbl1053.49032MR1862796
  4. [4] L.C. Evans, W. Gangbo, Differential equations methods for the Monge–Kantorovich mass transfer problem, Mem. Amer. Math. Soc.137 (653) (1999). Zbl0920.49004
  5. [5] W. Gangbo, The Monge mass transfer problem and its applications, Contemp. Math.226 (1999) 79-104. Zbl0930.49025MR1660743
  6. [6] L.V. Kantorovich, On the transfer of masses, Dokl. Akad. Nauk SSSR37 (1942) 227-229. 
  7. [7] L.V. Kantorovich, On a problem of Monge, Uspekhi Mat. Nauk3 (1948) 225-226. 
  8. [8] G. Monge, Memoire sur la Theorie des Déblais et des Remblais, Hist. de l'Acad. des Sciences de Paris, 1781. 
  9. [9] J.C. Oxtoby, Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc.24 (1970) 419-423. Zbl0187.00902MR260961
  10. [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. [11] S.T. Rachev, L. Rüschendorf, Mass Transportation Problems, Springer-Verlag, 1998. Zbl0990.60500
  12. [12] H.L. Royden, Real Analysis, second ed., Macmillan, 1968. Zbl0197.03501
  13. [13] N.S. Trudinger, X.J. Wang, On the Monge mass transfer problem, Calc. Var. Partial Differential Equations13 (2001) 19-31. Zbl1010.49030MR1854255

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