메뉴 건너뛰기




Volumn 125, Issue 2, 2004, Pages 207-241

Existence of optimal transport maps for crystalline norms

Author keywords

[No Author keywords available]

Indexed keywords


EID: 10044256416     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12521-7     Document Type: Article
Times cited : (65)

References (38)
  • 2
    • 10044247612 scopus 로고    scopus 로고
    • Lecture notes on optimal transport problems
    • (Funchal, Portugal, 2000), ed. P. Colli and J. F. Rodrigues, Lecture Notes in Math, Springer, Berlin
    • L. AMBROSIO, “Lecture notes on optimal transport problems” in Mathematical Aspects of Evolving Interfaces (Funchal, Portugal, 2000), ed. P. Colli and J. F. Rodrigues, Lecture Notes in Math. 1812, Springer, Berlin, 2003, 1-52.
    • (2003) Mathematical Aspects of Evolving Interfaces , vol.1812 , pp. 1-52
    • Ambrosio, L.1
  • 3
    • 10044286348 scopus 로고    scopus 로고
    • Existence and stability results in the L1 theory of optimal transportation
    • (Martina Franca, Italy, 2001), ed. L. A. Caffarelli and S. Salsa, Lecture Notes in Math, Springer, Berlin
    • 1 theory of optimal transportation” in Optimal Transportation and Applications (Martina Franca, Italy, 2001), ed. L. A. Caffarelli and S. Salsa, Lecture Notes in Math. 1813, Springer, Berlin, 2003, 123-160.
    • (2003) Optimal Transportation and Applications , vol.1813 , pp. 123-160
    • Ambrosio, L.1    Pratelli, A.2
  • 4
    • 0001482683 scopus 로고
    • Asymptotic development by T-convergence, Appl
    • G. ANZELLOTTI and S. BALDO, Asymptotic development by T-convergence, Appl. Math. Optim. 27 (1993), 105-123.
    • (1993) Math. Optim , vol.27 , pp. 105-123
    • Anzellotti, G.1    Baldo, S.2
  • 5
    • 10044295302 scopus 로고
    • Sur deux questions d’intégrabilité des fonctions
    • A. S. BESICOVITCH, Sur deux questions d’intégrabilité des fonctions, J. Soc. Phys.-Math. (Perm) 2 (1919), 105-123.
    • (1919) J. Soc. Phys.-Math. (Perm) , vol.2 , pp. 105-123
    • Besicovitch, A.S.1
  • 6
    • 0001016311 scopus 로고
    • Decomposition polaire et rearrangement monotone des champs de vecteurs
    • Y. BRENIER, Decomposition polaire et rearrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris Ser. I Math. 305 (1987), 805-808.
    • (1987) C. R. Acad. Sci. Paris Ser. I Math , vol.305 , pp. 805-808
    • Brenier, Y.1
  • 7
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Y. BRENIER, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math. 44 (1991), 375-417.
    • (1991) Comm. Pure Appl. Math , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 8
    • 84990563964 scopus 로고
    • Boundary regularity of maps with convex potentials
    • L. A. CAFFARELLI, Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. 45 (1992), 1141-1151.
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 1141-1151
    • Caffarelli, L.A.1
  • 9
    • 0036001762 scopus 로고    scopus 로고
    • Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
    • L. A. CAFFARELLI, M. FELDMAN, and 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.
    • (2002) J. Amer. Math. Soc , vol.15 , pp. 1-26
    • Caffarelli, L.A.1    Feldman, M.2    McCann, R.J.3
  • 10
    • 0003211244 scopus 로고
    • Convex Analysis and Measurable Multifunctions
    • Springer, Berlin
    • C. CASTAING and M. VALADIER, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
    • (1977) Lecture Notes in Math , vol.580
    • Castaing, C.1    Valadier, M.2
  • 11
    • 0035238703 scopus 로고    scopus 로고
    • How to make Davies’ theorem visible
    • M. CSORNYEI, How to make Davies’ theorem visible, Bull. London Math. Soc. 33 (2001), 59-66.
    • (2001) Bull. London Math. Soc , vol.33 , pp. 59-66
    • Csornyei, M.1
  • 13
    • 0007422672 scopus 로고
    • On accessibility of plane sets and differentiation of functions of two real variables
    • R. O. DAVIES, On accessibility of plane sets and differentiation of functions of two real variables, Proc. Cambridge Philos. Soc. 48 (1952), 215-232.
    • (1952) Proc. Cambridge Philos. Soc , vol.48 , pp. 215-232
    • Davies, R.O.1
  • 16
    • 0036556947 scopus 로고    scopus 로고
    • Regularity properties for Monge transport density and for solutions of some shape optimization problem
    • L. de PASCALE and A. PRATELLI, Regularity properties for Monge transport density and for solutions of some shape optimization problem, Calc. Var. Partial Differential Equations 14 (2002), 249-274.
    • (2002) Calc. Var. Partial Differential Equations , vol.14 , pp. 249-274
    • Pascale, L.1    Pratelli, A.2
  • 17
    • 0011604371 scopus 로고
    • Zur c-Konvexitãt und c-Subdifferenzierbarkeit von Funktionalen
    • H. DIETRICH, Zur c-Konvexitãt und c-Subdifferenzierbarkeit von Funktionalen, Optimization 19 (1988), 355-371.
    • (1988) Optimization , vol.19 , pp. 355-371
    • Dietrich, H.1
  • 18
    • 0003073688 scopus 로고    scopus 로고
    • Partial differential equations and Monge-Kantorovich mass transfer
    • (Cambridge, Mass., 1997), ed. R. Bott, A. Jaffe, D. Jerison, G. Lusztig, I. Singer, and S.-T. Yau, Int. Press, Boston
    • L. C. EVANS, “Partial differential equations and Monge-Kantorovich mass transfer” in Current Developments in Mathematics (Cambridge, Mass., 1997), ed. R. Bott, A. Jaffe, D. Jerison, G. Lusztig, I. Singer, and S.-T. Yau, Int. Press, Boston, 1999, 65-126.
    • (1999) Current Developments in Mathematics , pp. 65-126
    • Evans, L.C.1
  • 19
    • 0032622583 scopus 로고    scopus 로고
    • Differential equation methods for the Monge-Kantorovich mass transfer problem
    • L. C. EVANS and W. GANGBO, Differential equation methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc. 137 (1999), no. 653.
    • (1999) Mem. Amer. Math. Soc , vol.137 , Issue.653
    • Evans, L.C.1    Gangbo, W.2
  • 20
    • 0000803776 scopus 로고
    • The multiplier problem for the ball
    • C. FEFFERMAN, The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330-336.
    • (1971) Ann. of Math , vol.94 , Issue.2 , pp. 330-336
    • Fefferman, C.1
  • 21
    • 0036706666 scopus 로고    scopus 로고
    • Uniqueness and transport density in Monge’s mass transportation problem
    • M. FELDMAN and R. J. MCCANN, Uniqueness and transport density in Monge’s mass transportation problem, Calc. Var. Partial Differential Equations 15 (2002), 81-113.
    • (2002) Calc. Var. Partial Differential Equations , vol.15 , pp. 81-113
    • Feldman, M.1    McCann, R.J.2
  • 22
    • 21844484336 scopus 로고
    • An elementary proof of the polar factorization of vector-valued functions
    • W. GANGBO, An elementary proof of the polar factorization of vector-valued functions, Arch. Rational Mech. Anal. 128 (1994), 381-399.
    • (1994) Arch. Rational Mech. Anal , vol.128 , pp. 381-399
    • Gangbo, W.1
  • 23
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. GANGBO and R. J. MCCANN, The geometry of optimal transportation, Acta Math. 177 (1996), 113-161.
    • (1996) Acta Math , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 26
  • 27
    • 84976017472 scopus 로고
    • A compact set of disjoint line segments in E
    • 3 whose end set has positive measure, Mathematika 18 (1971), 112-125.
    • (1971) Mathematika , vol.18 , pp. 112-125
    • Larman, D.G.1
  • 28
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • R. J. MCCANN, Polar factorization of maps on Riemannian manifolds, Geom. Funct. Anal. 11 (2001), 589-608.
    • (2001) Geom. Funct. Anal , vol.11 , pp. 589-608
    • McCann, R.J.1
  • 30
    • 0011664990 scopus 로고
    • Sur la mesure des ensembles plans dont tous les point sont rectalineairement accesssibles
    • O. NIKODYM, Sur la mesure des ensembles plans dont tous les point sont rectalineairement accesssibles, Fundamenta Mathematicae 10 (1927), 116-168.
    • (1927) Fundamenta Mathematicae , vol.10 , pp. 116-168
    • Nikodym, O.1
  • 31
    • 0003696856 scopus 로고    scopus 로고
    • Mass Transportation Problems, Vol. I: Theory; Vol. II: Applications
    • Springer, New York
    • S. T. RACHEV and L. RÜSCHENDORF, Mass Transportation Problems, Vol. I: Theory; Vol. II: Applications, Probab. Appl., Springer, New York, 1998.
    • (1998) Probab. Appl.
    • Rachev, S.T.1    Rüschendorf, L.2
  • 32
    • 0030584978 scopus 로고    scopus 로고
    • On c-optimal random variables
    • L. RÜSCHENDORF, On c-optimal random variables, Statist. Probab. Lett. 27 (1996), 267-270.
    • (1996) Statist. Probab. Lett , vol.27 , pp. 267-270
    • Rüschendorf, L.1
  • 33
    • 0023291797 scopus 로고
    • Note on the optimal transportation of distributions
    • C. S. SMITH and M. KNOTT, Note on the optimal transportation of distributions, J. Optim. Theory Appl. 52 (1987), 323-329.
    • (1987) J. Optim. Theory Appl , vol.52 , pp. 323-329
    • Smith, C.S.1    Knott, M.2
  • 34
    • 0000012825 scopus 로고
    • On Hoeffding-Frechet bounds and cyclic monotone relations
    • C. S. SMITH and M. KNOTT, On Hoeffding-Frechet bounds and cyclic monotone relations, J. Multivariate Anal. 40 (1992), 328-334.
    • (1992) J. Multivariate Anal , vol.40 , pp. 328-334
    • Smith, C.S.1    Knott, M.2
  • 35
    • 0003299763 scopus 로고
    • Geometric problems in the theory of infinite-dimensional probability distributions
    • V. N. SUDAKOV, Geometric problems in the theory of infinite-dimensional probability distributions, Proc. Steklov Inst. Math. 1979, no. 2, 1-178.
    • (1979) Proc. Steklov Inst. Math , vol.2 , pp. 1-178
    • Sudakov, V.N.1
  • 38
    • 1542342359 scopus 로고    scopus 로고
    • Topics in Optimal Transportation
    • Amer. Math. Soc., Providence
    • C. VILLANI, Topics in Optimal Transportation, Grad. Stud. Math. 58, Amer. Math. Soc., Providence, 2003.
    • (2003) Grad. Stud. Math , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.