메뉴 건너뛰기




Volumn 34, Issue 2, 2009, Pages 193-231

A new class of transport distances between measures

Author keywords

[No Author keywords available]

Indexed keywords


EID: 54349105688     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-008-0182-5     Document Type: Article
Times cited : (198)

References (33)
  • 1
    • 33746866139 scopus 로고
    • Weak lower semicontinuous envelope of functionals defined on a space of measures
    • 4
    • L. Ambrosio G. Buttazzo 1988 Weak lower semicontinuous envelope of functionals defined on a space of measures Ann. Mat. Pura Appl. 150 4 311 339
    • (1988) Ann. Mat. Pura Appl. , vol.150 , pp. 311-339
    • Ambrosio, L.1    Buttazzo, G.2
  • 3
    • 33746157912 scopus 로고    scopus 로고
    • Gradient flows in metric spaces and in the space of probability measures
    • Birkhäuser Verlag, Basel
    • Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel (2005)
    • (2005) Lectures in Mathematics ETH Zürich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 5
    • 47549096195 scopus 로고    scopus 로고
    • Existence and stability for Fokker-Planck equations with log-concave reference measure
    • Prepriny, arxiv:0704.2458v1. (to appear)
    • Ambrosio, L., Savaré, G., Zambotti, L.: Existence and stability for Fokker-Planck equations with log-concave reference measure, Prepriny, arxiv:0704.2458v1. Probab. Theory Relat. Fields (2007) (to appear)
    • (2007) Probab. Theory Relat. Fields
    • Ambrosio, L.1    Savaré, G.2    Zambotti, L.3
  • 6
    • 0002042431 scopus 로고    scopus 로고
    • On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
    • A. Arnold P. Markowich G. Toscani A. Unterreiter 2001 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations Comm. Partial Differ. Equ. 26 43 100
    • (2001) Comm. Partial Differ. Equ. , vol.26 , pp. 43-100
    • Arnold, A.1    Markowich, P.2    Toscani, G.3    Unterreiter, A.4
  • 7
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • J.-D. Benamou Y. Brenier 2000 A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem Numer. Math. 84 375 393
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 8
    • 34250424671 scopus 로고
    • Convex measures on locally convex spaces
    • C. Borell 1974 Convex measures on locally convex spaces Ark. Mat. 12 239 252
    • (1974) Ark. Mat. , vol.12 , pp. 239-252
    • Borell, C.1
  • 10
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Y. Brenier 1991 Polar factorization and monotone rearrangement of vector-valued functions Comm. Pure Appl. Math. 44 375 417
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 13
    • 54349129004 scopus 로고    scopus 로고
    • Eulerian calculus for the displacement convexity in the Wasserstein distance
    • Preprint, arXiv:0801.2455v1. (to appear)
    • Daneri, S., Savaré, G.: Eulerian calculus for the displacement convexity in the Wasserstein distance. Preprint, arXiv:0801.2455v1. SIAM J. Math. Anal. (2008) (to appear)
    • (2008) SIAM J. Math. Anal.
    • Daneri, S.1    Savaré, G.2
  • 14
    • 0007106184 scopus 로고
    • New problems on minimizing movements
    • Baiocchi, C., Lions, J.L. (eds.) Masson
    • De Giorgi, E.: New problems on minimizing movements. In: Baiocchi, C., Lions, J.L. (eds.) Boundary Value Problems for PDE and Applications, pp. 81-98. Masson 1993
    • (1993) Boundary Value Problems for PDE and Applications , pp. 81-98
    • De Giorgi, E.1
  • 17
    • 0003073688 scopus 로고    scopus 로고
    • Partial differential equations and Monge-Kantorovich mass transfer
    • Int. Press, Boston
    • Evans, L.C.: Partial differential equations and Monge-Kantorovich mass transfer, in Current developments in mathematics, 1997, pp. 65-126. Int. Press, Boston (1999)
    • (1997) Current Developments in Mathematics , pp. 65-126
    • Evans, L.C.1
  • 18
    • 0032622583 scopus 로고    scopus 로고
    • Differential equations methods for the Monge-Kantorovich mass transfer problem
    • Evans, L.C., Gangbo, W.: Differential equations methods for the Monge-Kantorovich mass transfer problem. Mem. Am. Math. Soc. 137, viii+66 (1999)
    • (1999) Mem. Am. Math. Soc. , vol.137
    • Evans, L.C.1    Gangbo, W.2
  • 19
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • W. Gangbo R.J. McCann 1996 The geometry of optimal transportation Acta Math. 177 113 161
    • (1996) Acta Math. , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 20
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • (electronic)
    • R. Jordan D. Kinderlehrer F. Otto 1998 The variational formulation of the Fokker-Planck equation SIAM J. Math. Anal. 29 1 17 (electronic)
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 21
    • 23744474323 scopus 로고    scopus 로고
    • On a functional operation generating convex functions. I. Duality
    • P. Maréchal 2005 On a functional operation generating convex functions. I. Duality J. Optim. Theory Appl. 126 175 189
    • (2005) J. Optim. Theory Appl. , vol.126 , pp. 175-189
    • Maréchal, P.1
  • 22
    • 23844493140 scopus 로고    scopus 로고
    • On a functional operation generating convex functions. II. Algebraic properties
    • P. Maréchal 2005 On a functional operation generating convex functions. II. Algebraic properties J. Optim. Theory Appl. 126 357 366
    • (2005) J. Optim. Theory Appl. , vol.126 , pp. 357-366
    • Maréchal, P.1
  • 23
    • 0001636186 scopus 로고
    • 1 isometric imbeddings
    • 1 isometric imbeddings Ann. Math. 60 383 396
    • (1954) Ann. Math. , vol.60 , pp. 383-396
    • Nash, J.1
  • 24
    • 0002702476 scopus 로고
    • The imbedding problem for Riemannian manifolds
    • J Nash 1956 The imbedding problem for Riemannian manifolds Ann. Math. 63 20 63
    • (1956) Ann. Math. , vol.63 , pp. 20-63
    • Nash, J.1
  • 26
    • 0039525530 scopus 로고    scopus 로고
    • Evolution of microstructure in unstable porous media flow: A relaxational approach
    • F. Otto 1999 Evolution of microstructure in unstable porous media flow: a relaxational approach Comm. Pure Appl. Math. 52 873 915
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 873-915
    • Otto, F.1
  • 27
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto 2001 The geometry of dissipative evolution equations: the porous medium equation Comm. Partial Differ. Equ. 26 101 174
    • (2001) Comm. Partial Differ. Equ. , vol.26 , pp. 101-174
    • Otto, F.1
  • 28
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • F. Otto C. Villani 2000 Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality J. Funct. Anal. 173 361 400
    • (2000) J. Funct. Anal. , vol.173 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 29
    • 33746121129 scopus 로고    scopus 로고
    • Eulerian calculus for the contraction in the Wasserstein distance
    • (electronic)
    • F. Otto M. Westdickenberg 2005 Eulerian calculus for the contraction in the Wasserstein distance SIAM J. Math. Anal. 37 1227 1255 (electronic)
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 1227-1255
    • Otto, F.1    Westdickenberg, M.2
  • 31
    • 84972561023 scopus 로고
    • A general correspondence between dual minimax problems and convex problems
    • R. Rocckafellar 1968 A general correspondence between dual minimax problems and convex problems Pac. J. Math. 25 597 611
    • (1968) Pac. J. Math. , vol.25 , pp. 597-611
    • Rocckafellar, R.1
  • 32
    • 1542342359 scopus 로고    scopus 로고
    • Topics in optimal transportation
    • American Mathematical Society, Providence
    • Villani, C.: Topics in optimal transportation. In: Graduate Studies in Mathematics, vol. 58. American Mathematical Society, Providence (2003)
    • (2003) Graduate Studies in Mathematics , vol.58
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.