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Volumn 175, Issue 1, 2010, Pages 1-59

Optimal transportation on non-compact manifolds

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EID: 77949770332     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-010-0001-5     Document Type: Article
Times cited : (77)

References (43)
  • 2
    • 10044247612 scopus 로고    scopus 로고
    • Lecture notes on optimal transport problems, in Mathematical Aspects of Evolving Interfaces
    • Berlin/New York: Springer-Verlag
    • L. Ambrosio, Lecture notes on optimal transport problems, in Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics 1812, Springer-Verlag, Berlin/New York, 2003, pp. 1-52.
    • (2003) Lecture Notes in Mathematics , vol.1812 , pp. 1-52
    • Ambrosio, L.1
  • 3
    • 0000467856 scopus 로고
    • Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands
    • L. Ambrosio, O. Ascenzi and G. Buttazzo, Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands, Journal of Mathematical Analysis and Applications 142 (1989), 301-316.
    • (1989) Journal of Mathematical Analysis and Applications , vol.142 , pp. 301-316
    • Ambrosio, L.1    Ascenzi, O.2    Buttazzo, G.3
  • 6
    • 84941449805 scopus 로고
    • Analytische Eigenschaften konvexer Funktionen auf Riemannschen Manigfaltigkeiten
    • V. Bangert, Analytische Eigenschaften konvexer Funktionen auf Riemannschen Manigfaltigkeiten, Journal für die Reine und Angewandte Mathematik 307 (1979), 309-324.
    • (1979) Journal für Die Reine Und Angewandte Mathematik , vol.307 , pp. 309-324
    • Bangert, V.1
  • 8
    • 33749057063 scopus 로고    scopus 로고
    • The Monge problem for supercritical Mañé potential on compact manifolds
    • P. Bernard and B. Buffoni, The Monge problem for supercritical Mañé potential on compact manifolds, Advances in Mathematics 207 (2006), 691-706.
    • (2006) Advances in Mathematics , vol.207 , pp. 691-706
    • Bernard, P.1    Buffoni, B.2
  • 9
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics 44 (1991), 375-417.
    • (1991) Communications on Pure and Applied Mathematics , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 11
    • 0036001762 scopus 로고    scopus 로고
    • Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs
    • L. Caffarelli, M. Feldman and R. J. McCann, Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs. Journal of the American Mathematical Society 15 (2002), 1-26.
    • (2002) Journal of the American Mathematical Society , vol.15 , pp. 1-26
    • Caffarelli, L.1    Feldman, M.2    McCann, R.J.3
  • 12
    • 72449201783 scopus 로고    scopus 로고
    • Lecture Notes in Mathematics, L. A. Caffarelli and S. Salsa (Eds.), Berlin: Springer-Verlag
    • L. A. Caffarelli and S. Salsa, Editors, Optimal transportation and applications, Lecture Notes in Mathematics 1813, Lectures from the C. I. M. E. Summer School held in Martina Franca, September 2-8, 2001, Springer-Verlag, Berlin, 2003.
    • (2003) Optimal Transportation and Applications , vol.1813
  • 14
    • 0003225812 scopus 로고
    • Methods of Dynamic and Nonsmooth Optimization
    • Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM)
    • F. H. Clarke, Methods of Dynamic and Nonsmooth Optimization, CBMS-NSF Regional Conference Series in Applied Mathematics 57, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989.
    • (1989) CBMS-NSF Regional Conference Series in Applied Mathematics
    • Clarke, F.H.1
  • 16
    • 84966256938 scopus 로고
    • Regularity properties of solutions to the basic problem in the calculus of variations
    • F. H. Clarke and R. B. Vinter, Regularity properties of solutions to the basic problem in the calculus of variations, Transactions of the American Mathematical Society 289 (1985), 73-98.
    • (1985) Transactions of the American Mathematical Society , vol.289 , pp. 73-98
    • Clarke, F.H.1    Vinter, R.B.2
  • 17
    • 0004179050 scopus 로고
    • Mass: Birkhäuser Boston
    • D. L. Cohn, Measure theory, Birkhäuser Boston, Mass, 1980.
    • (1980) Measure Theory
    • Cohn, D.L.1
  • 18
    • 0003073688 scopus 로고    scopus 로고
    • Partial differential equations and Monge-Kantorovich mass transfer
    • R. Bott et al., eds, Cambridge: International Press
    • L. C. Evans, Partial differential equations and Monge-Kantorovich mass transfer, in Current Developments in Mathematics (R. Bott et al., eds.), International Press, Cambridge, 1997, pp. 26-78.
    • (1997) Current Developments in Mathematics , pp. 26-78
    • Evans, L.C.1
  • 19
    • 0032622583 scopus 로고    scopus 로고
    • Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem
    • L. C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem, Memoirs of the American Mathematical Society 137, (1999).
    • (1999) Memoirs of the American Mathematical Society , pp. 137
    • Evans, L.C.1    Gangbo, W.2
  • 26
    • 0012941525 scopus 로고    scopus 로고
    • The Monge mass transfer problem and its applications
    • Contemporary Mathematics, Providence, RI: American Mathematical Society
    • W. Gangbo, The Monge mass transfer problem and its applications, in Monge Ampère equation: applications to geometry and optimization, Contemporary Mathematics 226, American Mathematical Society, Providence, RI, 1999, pp. 79-104.
    • (1999) Monge Ampère Equation: Applications to Geometry and Optimization , vol.226 , pp. 79-104
    • Gangbo, W.1
  • 27
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. Gangbo and R. J. McCann, The geometry of optimal transportation. Acta Mathematica 177 (1996), 113-161.
    • (1996) Acta Mathematica , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 32
    • 0000456667 scopus 로고
    • Existence of quasiperiodic orbits for twist homeomorphisms of the annulus
    • J. N. Mather, Existence of quasiperiodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), 457-467.
    • (1982) Topology , vol.21 , pp. 457-467
    • Mather, J.N.1
  • 33
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • R. McCann, Polar factorization of maps on Riemannian manifolds, Geometric and Functional Analysis 11 (2001), no. 3, 589-608.
    • (2001) Geometric and Functional Analysis , vol.11 , Issue.3 , pp. 589-608
    • McCann, R.1
  • 34
    • 0002259889 scopus 로고
    • Mémoire sur la Théorie des Déblais et des Remblais
    • G. Monge, Mémoire sur la Théorie des Déblais et des Remblais, Hist. de l'Acad. des Sciences de Paris (1781), 666-704.
    • (1781) Hist. de l'Acad. des Sciences de Paris , pp. 666-704
    • Monge, G.1
  • 35
    • 47249130466 scopus 로고    scopus 로고
    • Selected chapters in the calculus of variations
    • Lecture Notes by Oliver Knill, Basel: Birkhäuser Verlag
    • J. Moser, Selected chapters in the calculus of variations, in Lectures in Mathematics ETH Zürich, Lecture Notes by Oliver Knill, Birkhäuser Verlag, Basel, 2003.
    • (2003) Lectures in Mathematics ETH Zürich
    • Moser, J.1
  • 37
    • 0003696856 scopus 로고    scopus 로고
    • Mass transportation problems, Vol. I: Theory, Vol. II: Applications
    • New York: Springer-Verlag
    • S. T. Rachev and L. Rüschendorf, Mass transportation problems, Vol. I: Theory, Vol. II: Applications. in Probability and its Applications, Springer-Verlag, New York, 1998.
    • (1998) Probability and Its Applications
    • Rachev, S.T.1    Rüschendorf, L.2
  • 39
    • 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, Proceedings of the Steklov Institute of Mathematics 141 (1979), 1-178.
    • (1979) Proceedings of the Steklov Institute of Mathematics , vol.141 , pp. 1-178
    • Sudakov, V.N.1
  • 41
    • 2442557820 scopus 로고    scopus 로고
    • Topics in mass transportation
    • Providence, RI: American Mathematical Society
    • C. Villani, Topics in mass transportation, Graduate Studies in Mathematics 58, American Mathematical Society, Providence, RI, 2004.
    • (2004) Graduate Studies in Mathematics
    • Villani, C.1
  • 43
    • 0004284115 scopus 로고    scopus 로고
    • Boston, MA: Systems & Control: Foundations & Applications, Birkhäuser Boston Inc
    • R. Vinter, Optimal control, Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA, 2000.
    • (2000) Optimal Control
    • Vinter, R.1


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