How to show that some rays are maximal transport rays in Monge Problem
Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 179-201. 
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     author = {Pratelli, Aldo},
     title = {How to show that some rays are maximal transport rays in {Monge} {Problem}},
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     volume = {113},
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Pratelli, Aldo. How to show that some rays are maximal transport rays in Monge Problem. Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005), pp. 179-201. http://www.numdam.org/item/RSMUP_2005__113__179_0/

[1] L. Ambrosio, Lecture Notes on Optimal Transport Problems, in Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics, LNM 1812, Springer (2003), pp. 1-52. | MR | Zbl

[2] L. Ambrosio - A. Pratelli, Existence and stability results in the L1 theory of optimal transportation, in Optimal Transportation and Applications, Lecture Notes in Mathematics, LNM 1813, Springer (2003), pp. 123-160. | MR | Zbl

[3] L. Ambrosio - N. Fusco - D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press (2000). | MR | Zbl

[4] G. Bouchitté - G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich Equation, J. Eur. Math. Soc., 3 (2001), pp. 139-168. | MR | Zbl

[5] G. Bouchitté - G. Buttazzo P. SEPPECHER, Shape optimization solutions via Monge-Kantorovich equation, C.R. Acad. Sci. Paris, 324-I (1997), pp. 1185-1191. | MR | Zbl

[6] C. Castaing - M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, 580, Springer (1977). | MR | Zbl

[7] L.C. Evans - W. Gangbo, Differential equations methods for the MongeKantorovich mass transfer problem, Memoirs of the A.M.S., Vol. 137, Number 653, (1999). | MR | Zbl

[8] I. Fragalà, M.S. Gelli - A. Pratelli, Continuity of an optimal transport in Monge problem, to appear on JMPA. | MR | Zbl

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

[10] L.V. Kantorovich, On a problem of Monge, Uspekhi Mat. Nauk., 3 (1948), pp. 225-226.

[11] G. Monge, Memoire sur la Theorie des Déblais et des Remblais, Hist. de l'Acad. des Sciences de Paris (1781).

[12] 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). Avalaible on http://cvgmt.sns.it/ .

[13] S.T. Rachev - L. Rüschendorf, Mass Transportation Problems, SpringerVerlag (1998).