@article{ZNSL_2004_312_a13,
author = {V. L. Levin},
title = {Optimality conditions and exact solutions to the two-dimensional {Monge{\textendash}Kantorovich} problem},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {150--164},
year = {2004},
volume = {312},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a13/}
}
V. L. Levin. Optimality conditions and exact solutions to the two-dimensional Monge–Kantorovich problem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 150-164. http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a13/
[1] L. Ambrosio, “Lecture notes on optimal transport problems”, Mathematical Aspects of Evolving Interfaces, Lecture Notes in Math., 1812, eds. P. Colli, J. F. Rodrigues, 2003, 1–52 | MR | Zbl
[2] L. Ambrosio, B. Kirchheim, A. Pratelli, “Existence of optimal transport maps for crystalline norms”, Duke Math. J., 125:2 (2004), 207–241 | DOI | MR | Zbl
[3] Y. Brenier, “Polar factorization and monotone rearrangement of vector-valued functions”, Comm. Pure. Appl. Math., 44 (1991), 375–417 | DOI | MR | Zbl
[4] A. M. Vershik, “Neskolko zamechanii o beskonechnomernykh zadachakh lineinogo programmirovaniya”, UMN, 25:5 (1970), 117–124
[5] W. Gangbo, R. J. McCann, “The geometry of optimal transportation”, Acta Math., 177 (1966), 113–161 | DOI | MR
[6] L. V. Kantorovich, “O peremeschenii mass”, DAN SSSR, 37:7–8 (1942), 199–201 | MR
[7] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl
[8] L. V. Kantorovich, G. Sh. Rubinshtein, “Ob odnom prostranstve vpolne additivnykh funktsii”, Vestnik LGU. Ser. matem., mekh. i astr., 13:7 (1958), 52–59 | MR | Zbl
[9] 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 | DOI | MR | Zbl
[10] V. L. Levin, “Dvoistvennost i approksimatsiya v zadache o peremeschenii mass”, Matematicheskaya ekonomika i funktsionalnyi analiz, Nauka, M., 1974, 94–108 | MR
[11] V. L. Levin, “Formula dlya optimalnogo znacheniya zadachi Monzha–Kantorovicha s gladkoi funktsiei stoimosti i kharakterizatsiya tsiklicheski monotonnykh otobrazhenii”, Matem. sb., 181:12 (1990), 1694–1709 | MR
[12] V. L. Levin, “General Monge–Kantorovich problem and its applications in measure theory and mathematical economics”, Functional Analysis, Optimization, and Mathematical Economics, A Collection of Papers Dedicated to the Memory of L. V. Kantorovich, ed. Leifman L. J., Oxford Univ. Press, New York–Oxford, 1990, 141–176 | MR | Zbl
[13] V. L. Levin, “A superlinear multifunction arising in connection with mass transfer problems”, Set-Valued Analysis, 4 (1996), 41–65 | DOI | MR | Zbl
[14] V. L. Levin, “Reduced cost functions and their applications”, J. Math. Econ., 28 (1997), 155–186 | DOI | MR | Zbl
[15] V. L. Levin, “K teorii dvoistvennosti dlya netopologicheskikh variantov zadachi o peremeschenii mass”, Matem. sb., 188:4 (1997), 95–126 | MR | Zbl
[16] V. L. Levin, “Abstract cyclical monotonicity and Monge solutions for the general Monge–Kantorovich problem”, Set-Valued Analysis, 7 (1999), 7–32 | DOI | MR | Zbl
[17] V. L. Levin, “The Monge–Kantorovich problems and stochastic preference relations”, Adv. Math. Econ., 3 (2001), 97–124 | MR | Zbl
[18] V. L. Levin, “Usloviya optimalnosti dlya gladkikh reshenii Monzha zadachi Monzha–Kantorovicha”, Funkts. analiz i ego pril., 36:2 (2002), 38–44 | MR | Zbl
[19] V. L. Levin, “Reshenie zadach Monzha i Monzha–Kantorovicha. Teoriya i primery”, DAN, 388:1 (2003), 7–10 | MR | Zbl
[20] V. L. Levin, “Optimal solutions of the Monge problem”, Adv. Math. Econ., 6 (2004), 85–122 | MR | Zbl
[21] V. L. Levin, A. A. Milyutin, “Zadacha o peremeschenii mass s razryvnoi funktsiei stoimosti i massovaya postanovka problemy dvoistvennosti vypuklykh ekstremalnykh zadach”, UMN, 34:3 (1979), 3–68 | MR | Zbl
[22] R. J. McCann, “Exact solutions to the transportation problem on the line”, Proc. Royal Soc. London A, 455 (1999), 1341–1380 | DOI | MR | Zbl
[23] G. Monge, “Mémoire sur la théorie des déblais et de remblais”, Histoire de l'Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année, 1781, 666–704
[24] A. Yu. Plakhov, “Zadacha Nyutona o tele naimenshego usrednennogo soprotivleniya”, Matem. sb., 195:7 (2004), 105–126 | MR | Zbl
[25] A. Yu. Plakhov, “Tochnye resheniya odnomernoi zadachi Monzha–Kantorovicha”, Matem. sb., 195:9 (2004), 57–74 | MR | Zbl
[26] S. T. Rachev, L. Rüschendorf, Mass Transportation Problems. V. 1: Theory, V. 2: Applications, Springer, Berlin, 1998 | Zbl
[27] L. Rüschendorf, S. T. Rachev, “A characterization of random variables with minimum $L^2$-distance”, J. Multivariate Anal., 32 (1990), 48–54 | DOI | MR | Zbl
[28] V. N. Sudakov, Geometricheskie problemy teorii beskonechnomernykh veroyatnostnykh raspredelenii, Trudy MIAN, 141, 1976 | MR | Zbl
[29] N. S. Trudinger, X. J. Wang, “On the Monge mass transfer problem”, Calc. Var. PDE, 13 (2001), 19–31 | DOI | MR | Zbl
[30] L. Uckelmann, “Optimal couplings between one-dimensional distributions”, Distributions with Given Marginals and Moment Problems, eds. V. Beneš, J. Štěpán, Kluwer, Dordrecht, 1997, 275–281 | MR | Zbl