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Volumn 3, Issue , 2007, Pages 1-136

Chapter 1 Gradient Flows of Probability Measures

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EID: 66049132812     PISSN: 18745717     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5717(07)80004-1     Document Type: Chapter
Times cited : (61)

References (87)
  • 1
    • 0141682220 scopus 로고    scopus 로고
    • Asymptotic behavior for doubly degenerate parabolic equations
    • Agueh M. Asymptotic behavior for doubly degenerate parabolic equations. C. R. Math. Acad. Sci. Paris 337 (2003) 331-336
    • (2003) C. R. Math. Acad. Sci. Paris , vol.337 , pp. 331-336
    • Agueh, M.1
  • 2
    • 31744435328 scopus 로고    scopus 로고
    • Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
    • Agueh M. Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory. Adv. Differential Equations 10 (2005) 309-360
    • (2005) Adv. Differential Equations , vol.10 , pp. 309-360
    • Agueh, M.1
  • 3
    • 0041828253 scopus 로고    scopus 로고
    • The optimal evolution of the free energy of interacting gases and its applications
    • Agueh M., Ghoussoub N., and Kang X. The optimal evolution of the free energy of interacting gases and its applications. C. R. Math. Acad. Sci. Paris 337 (2003) 173-178
    • (2003) C. R. Math. Acad. Sci. Paris , vol.337 , pp. 173-178
    • Agueh, M.1    Ghoussoub, N.2    Kang, X.3
  • 5
    • 0003123787 scopus 로고
    • A theorem on triangles in a metric space and some of its applications
    • Aleksandrov A.D. A theorem on triangles in a metric space and some of its applications. Trudy Mat. Inst. Steklov. 38 (1951) 5-23
    • (1951) Trudy Mat. Inst. Steklov. , vol.38 , pp. 5-23
    • Aleksandrov, A.D.1
  • 8
    • 0003282839 scopus 로고    scopus 로고
    • Functions of Bounded Variation and Free Discontinuity Problems
    • Clarendon, Oxford
    • Ambrosio L., Fusco N., and Pallara D. Functions of Bounded Variation and Free Discontinuity Problems. Oxford Math. Monogr. (2000), Clarendon, Oxford
    • (2000) Oxford Math. Monogr.
    • Ambrosio, L.1    Fusco, N.2    Pallara, D.3
  • 9
    • 33746157912 scopus 로고    scopus 로고
    • Gradient Flows in Metric Spaces and in the Spaces of Probability Measures
    • Birkhäuser, Basel
    • Ambrosio L., Gigli N., and Savaré G. Gradient Flows in Metric Spaces and in the Spaces of Probability Measures. Lectures Math. ETH Zürich (2005), Birkhäuser, Basel
    • (2005) Lectures Math. ETH Zürich
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 10
    • 66049103168 scopus 로고    scopus 로고
    • Stability of Flows Associated to Gradient Vector Fields and Convergence of Iterated Transport Maps
    • to appear
    • L. Ambrosio, S. Lisini and G. Savaré, Stability of Flows Associated to Gradient Vector Fields and Convergence of Iterated Transport Maps, Manuscripta Math., to appear.
    • Manuscripta Math
    • Ambrosio, L.1    Lisini, S.2    Savaré, G.3
  • 11
    • 33744960321 scopus 로고    scopus 로고
    • Topics on Analysis in Metric Spaces
    • Oxford Univ. Press, Oxford
    • Ambrosio L., and Tilli P. Topics on Analysis in Metric Spaces. Oxford Lecture Ser. Math. Appl. Vol. 25 (2004), Oxford Univ. Press, Oxford
    • (2004) Oxford Lecture Ser. Math. Appl. , vol.25
    • Ambrosio, L.1    Tilli, P.2
  • 12
    • 21744436651 scopus 로고    scopus 로고
    • Refined convex Sobolev inequalities
    • Arnold A., and Dolbeault J. Refined convex Sobolev inequalities. J. Funct. Anal. 225 (2005) 337-351
    • (2005) J. Funct. Anal. , vol.225 , pp. 337-351
    • Arnold, A.1    Dolbeault, J.2
  • 13
    • 0002042431 scopus 로고    scopus 로고
    • On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
    • Arnold A., Markowich P., Toscani G., and Unterreiter A. On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Comm. Partial Differential Equations 26 (2001) 43-100
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 43-100
    • Arnold, A.1    Markowich, P.2    Toscani, G.3    Unterreiter, A.4
  • 14
    • 0002552584 scopus 로고
    • Discretization of evolution variational inequalities
    • Colombini F., Marino A., Modica L., and Spagnolo S. (Eds), Birkhäuser, Boston, MA
    • Baiocchi C. Discretization of evolution variational inequalities. In: Colombini F., Marino A., Modica L., and Spagnolo S. (Eds). Partial Differential Equations and the Calculus of Variations Vol. I (1989), Birkhäuser, Boston, MA 59-92
    • (1989) Partial Differential Equations and the Calculus of Variations , vol.I , pp. 59-92
    • Baiocchi, C.1
  • 15
    • 0034407460 scopus 로고    scopus 로고
    • A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
    • Benamou J.-D., and Brenier Y. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375-393
    • (2000) Numer. Math. , vol.84 , pp. 375-393
    • Benamou, J.-D.1    Brenier, Y.2
  • 16
    • 0002028536 scopus 로고
    • Solutions intégrales d'équations d'évolution dans un espace de Banach
    • Bénilan P. Solutions intégrales d'équations d'évolution dans un espace de Banach. C. R. Acad. Sci. Paris 274 (1972) A47-A50
    • (1972) C. R. Acad. Sci. Paris , vol.274
    • Bénilan, P.1
  • 18
    • 0003323244 scopus 로고    scopus 로고
    • Gaussian Measures
    • Amer. Math. Soc., Providence, RI
    • Bogachev V.I. Gaussian Measures. Math. Surveys Monogr. Vol. 62 (1998), Amer. Math. Soc., Providence, RI
    • (1998) Math. Surveys Monogr. , vol.62
    • Bogachev, V.I.1
  • 19
    • 0009886850 scopus 로고    scopus 로고
    • Kinetic Equations and Asymptotic Theory
    • Benoit L., and Desvillettes P. (Eds), Gauthier-Villars, Éd. Sci. Méd. Elsevier, Paris Edited and with a foreword by
    • Bouchut F., Golse F., and Pulvirenti M. Kinetic Equations and Asymptotic Theory. In: Benoit L., and Desvillettes P. (Eds). Ser. Appl. Math. (Paris) (2000), Gauthier-Villars, Éd. Sci. Méd. Elsevier, Paris Edited and with a foreword by
    • (2000) Ser. Appl. Math. (Paris)
    • Bouchut, F.1    Golse, F.2    Pulvirenti, M.3
  • 20
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Brenier Y. 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
  • 21
    • 0002239265 scopus 로고
    • Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations
    • Univ. of Wisconsin Press, Madison Academic Press, New York (1971)
    • Brézis H. Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Contribution to Nonlinear Functional Analysis, Proc. Sympos. Math. Res. Center (1971), Univ. of Wisconsin Press, Madison 101-156 Academic Press, New York (1971)
    • (1971) Contribution to Nonlinear Functional Analysis, Proc. Sympos. Math. Res. Center , pp. 101-156
    • Brézis, H.1
  • 22
    • 0003282411 scopus 로고
    • Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
    • North-Holland, Amsterdam (50)
    • Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Math. Stud., Vol. 5, Notas de Matemática (1973), North-Holland, Amsterdam (50)
    • (1973) North-Holland Math. Stud., Vol. 5, Notas de Matemática
    • Brézis, H.1
  • 24
    • 0003238886 scopus 로고
    • Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations
    • Longman, Harlow
    • Buttazzo G. Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Res. Notes Math. Ser. Vol. 207 (1989), Longman, Harlow
    • (1989) Pitman Res. Notes Math. Ser. , vol.207
    • Buttazzo, G.1
  • 25
    • 0036021909 scopus 로고    scopus 로고
    • Homogeneous cooling states are not always good approximations to granular flows
    • Caglioti E., and Villani C. Homogeneous cooling states are not always good approximations to granular flows. Arch. Ration. Mech. Anal. 163 (2002) 329-343
    • (2002) Arch. Ration. Mech. Anal. , vol.163 , pp. 329-343
    • Caglioti, E.1    Villani, C.2
  • 26
    • 0037821662 scopus 로고    scopus 로고
    • Constrained steepest descent in the 2-Wasserstein metric
    • Carlen E.A., and Gangbo W. Constrained steepest descent in the 2-Wasserstein metric. Ann. of Math. (2) 157 (2003) 807-846
    • (2003) Ann. of Math. (2) , vol.157 , pp. 807-846
    • Carlen, E.A.1    Gangbo, W.2
  • 27
    • 2142661459 scopus 로고    scopus 로고
    • Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric
    • Carlen E.A., and Gangbo W. Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric. Arch. Ration. Mech. Anal. 172 (2004) 21-64
    • (2004) Arch. Ration. Mech. Anal. , vol.172 , pp. 21-64
    • Carlen, E.A.1    Gangbo, W.2
  • 28
    • 1542399709 scopus 로고    scopus 로고
    • Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
    • Carrillo J.A., McCann R.J., and Villani C. Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19 (2003) 971-1018
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 971-1018
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 29
    • 32544445429 scopus 로고    scopus 로고
    • Contractions in the 2-Wasserstein space and thermalization of granular media
    • Carrillo J.A., McCann R.J., and Villani C. Contractions in the 2-Wasserstein space and thermalization of granular media. Arch. Ration. Mech. Anal. (2006)
    • (2006) Arch. Ration. Mech. Anal.
    • Carrillo, J.A.1    McCann, R.J.2    Villani, C.3
  • 30
    • 0036026066 scopus 로고    scopus 로고
    • Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
    • Chasseigne E., and Vazquez J.L. Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities. Arch. Ration. Mech. Anal. 164 (2002) 133-187
    • (2002) Arch. Ration. Mech. Anal. , vol.164 , pp. 133-187
    • Chasseigne, E.1    Vazquez, J.L.2
  • 31
    • 1242299735 scopus 로고    scopus 로고
    • A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities
    • Cordero-Erausquin D., Nazaret B., and Villani C. A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182 (2004) 307-332
    • (2004) Adv. Math. , vol.182 , pp. 307-332
    • Cordero-Erausquin, D.1    Nazaret, B.2    Villani, C.3
  • 32
    • 0000018252 scopus 로고
    • Generation of semi-groups of nonlinear transformations on general Banach spaces
    • Crandall M.G., and Liggett T.M. Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93 (1971) 265-298
    • (1971) Amer. J. Math. , vol.93 , pp. 265-298
    • Crandall, M.G.1    Liggett, T.M.2
  • 33
    • 0012684812 scopus 로고
    • Semi-groups of nonlinear contractions and dissipative sets
    • Crandall M.G., and Pazy A. Semi-groups of nonlinear contractions and dissipative sets. J. Funct. Analysis 3 (1969) 376-418
    • (1969) J. Funct. Analysis , vol.3 , pp. 376-418
    • Crandall, M.G.1    Pazy, A.2
  • 34
    • 1542511259 scopus 로고    scopus 로고
    • Elliptic operators with unbounded drift coefficients and Neumann boundary condition
    • Da Prato G., and Lunardi A. Elliptic operators with unbounded drift coefficients and Neumann boundary condition. J. Differential Equations 198 (2004) 35-52
    • (2004) J. Differential Equations , vol.198 , pp. 35-52
    • Da Prato, G.1    Lunardi, A.2
  • 35
    • 0042864898 scopus 로고    scopus 로고
    • Second Order Partial Differential Equations in Hilbert Spaces
    • Cambridge Univ. Press, Cambridge
    • Da Prato G., and Zabczyk J. Second Order Partial Differential Equations in Hilbert Spaces. London Math. Soc. Lecture Notes Ser. Vol. 293 (2002), Cambridge Univ. Press, Cambridge
    • (2002) London Math. Soc. Lecture Notes Ser. , vol.293
    • Da Prato, G.1    Zabczyk, J.2
  • 36
    • 0007106184 scopus 로고
    • New problems on minimizing movements
    • Baiocchi C., and Lions J.L. (Eds), Masson
    • De Giorgi E. New problems on minimizing movements. In: Baiocchi C., and Lions J.L. (Eds). Boundary Value Problems for PDE and Applications (1993), Masson 81-98
    • (1993) Boundary Value Problems for PDE and Applications , pp. 81-98
    • De Giorgi, E.1
  • 38
    • 0000741384 scopus 로고
    • Evolution equations with lack of convexity
    • Degiovanni M., Marino A., and Tosques M. Evolution equations with lack of convexity. Nonlinear Anal. 9 (1985) 1401-1443
    • (1985) Nonlinear Anal. , vol.9 , pp. 1401-1443
    • Degiovanni, M.1    Marino, A.2    Tosques, M.3
  • 41
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • DiPerna R.J., and Lions P.-L. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511-547
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.-L.2
  • 44
    • 0003346795 scopus 로고
    • Measure Theory and Fine Properties of Functions
    • CRC Press, Boca Raton, FL
    • Evans L.C., and Gariepy R.F. Measure Theory and Fine Properties of Functions. Stud. Adv. Math. (1992), CRC Press, Boca Raton, FL
    • (1992) Stud. Adv. Math.
    • Evans, L.C.1    Gariepy, R.F.2
  • 45
    • 0003372936 scopus 로고
    • Geometric Measure Theory
    • Springer-Verlag, New York
    • Federer H. Geometric Measure Theory. Grundlehren Math. Wiss. Bd 153 (1969), Springer-Verlag, New York
    • (1969) Grundlehren Math. Wiss. , vol.Bd 153
    • Federer, H.1
  • 46
    • 66049108203 scopus 로고    scopus 로고
    • A Hamilton-Jacobi theory for controlled gradient flows in infinite dimensions
    • Feng J., and Katsoulakis M. A Hamilton-Jacobi theory for controlled gradient flows in infinite dimensions. Technical report (2003)
    • (2003) Technical report
    • Feng, J.1    Katsoulakis, M.2
  • 48
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • Gangbo W., and McCann R.J. 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
  • 49
    • 0035997406 scopus 로고    scopus 로고
    • The Brunn-Minkowski inequality
    • Gardner R. The Brunn-Minkowski inequality. Bull. Amer. Math. Soc. 39 (2002) 355-405
    • (2002) Bull. Amer. Math. Soc. , vol.39 , pp. 355-405
    • Gardner, R.1
  • 50
    • 0346491845 scopus 로고    scopus 로고
    • Variational formulation for the lubrication approximation of the Hele-Shaw flow
    • Giacomelli L., and Otto F. Variational formulation for the lubrication approximation of the Hele-Shaw flow. Calc. Var. Partial Differential Equations 13 (2001) 377-403
    • (2001) Calc. Var. Partial Differential Equations , vol.13 , pp. 377-403
    • Giacomelli, L.1    Otto, F.2
  • 51
    • 21144433755 scopus 로고    scopus 로고
    • Rigorous lubrication approximation
    • Giacomelli L., and Otto F. Rigorous lubrication approximation. Interfaces Free Bound. 5 (2003) 483-529
    • (2003) Interfaces Free Bound. , vol.5 , pp. 483-529
    • Giacomelli, L.1    Otto, F.2
  • 52
    • 37349061187 scopus 로고    scopus 로고
    • The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation
    • IMATI-CNR, Pavia
    • Gianazza U., Toscani G., and Savaré G. The Wasserstein gradient flow of the Fisher information and the Quantum Drift-Diffusion equation. Technical report (2006), IMATI-CNR, Pavia
    • (2006) Technical report
    • Gianazza, U.1    Toscani, G.2    Savaré, G.3
  • 54
    • 0242276328 scopus 로고    scopus 로고
    • A diffuse interface approach to Hele-Shaw flow
    • Glasner K. A diffuse interface approach to Hele-Shaw flow. Nonlinearity 16 (2003) 49-66
    • (2003) Nonlinearity , vol.16 , pp. 49-66
    • Glasner, K.1
  • 55
    • 84972542010 scopus 로고
    • Sublinear functions of measures and variational integrals
    • Goffman C., and Serrin J. Sublinear functions of measures and variational integrals. Duke Math. J. 31 (1964) 159-178
    • (1964) Duke Math. J. , vol.31 , pp. 159-178
    • Goffman, C.1    Serrin, J.2
  • 56
    • 0034204570 scopus 로고    scopus 로고
    • Variational formulations for Vlasov-Poisson-Fokker-Planck systems
    • Huang C., and Jordan R. Variational formulations for Vlasov-Poisson-Fokker-Planck systems. Math. Methods Appl. Sci. 23 (2000) 803-843
    • (2000) Math. Methods Appl. Sci. , vol.23 , pp. 803-843
    • Huang, C.1    Jordan, R.2
  • 57
    • 0032343437 scopus 로고    scopus 로고
    • The variational formulation of the Fokker-Planck equation
    • (electronic)
    • Jordan R., Kinderlehrer D., and Otto F. The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17 (electronic)
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1-17
    • Jordan, R.1    Kinderlehrer, D.2    Otto, F.3
  • 58
    • 0003333358 scopus 로고    scopus 로고
    • Nonpositive Curvature: Geometric and Analytic Aspects
    • Birkhäuser, Basel
    • Jost J. Nonpositive Curvature: Geometric and Analytic Aspects. Lectures Math. ETH Zürich, (1997), Birkhäuser, Basel
    • (1997) Lectures Math. ETH Zürich
    • Jost, J.1
  • 59
    • 0033468031 scopus 로고    scopus 로고
    • Approximation of parabolic equations using the Wasserstein metric
    • Kinderlehrer D., and Walkington N.J. Approximation of parabolic equations using the Wasserstein metric. M2AN Math. Model. Numer. Anal. 33 (1999) 837-852
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , pp. 837-852
    • Kinderlehrer, D.1    Walkington, N.J.2
  • 60
    • 0021421774 scopus 로고
    • On the optimal mapping of distributions
    • Knott M., and Smith C.S. On the optimal mapping of distributions. J. Optim. Theory Appl. 43 (1984) 39-49
    • (1984) J. Optim. Theory Appl. , vol.43 , pp. 39-49
    • Knott, M.1    Smith, C.S.2
  • 61
    • 84972544461 scopus 로고
    • Nonlinear semi-groups in Hilbert space
    • Kōmura Y. Nonlinear semi-groups in Hilbert space. J. Math. Soc. Japan 19 (1967) 493-507
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 493-507
    • Komura, Y.1
  • 62
    • 66049131389 scopus 로고    scopus 로고
    • Ricci curvature for metric-measure spaces via optimal transport
    • to appear
    • J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Comm. Pure Appl. Math., to appear.
    • Comm. Pure Appl. Math
    • Lott, J.1    Villani, C.2
  • 64
    • 0001225520 scopus 로고
    • Curves of maximal slope and parabolic variational inequalities on nonconvex constraints
    • Marino A., Saccon C., and Tosques M. Curves of maximal slope and parabolic variational inequalities on nonconvex constraints. Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 16 (1989) 281-330
    • (1989) Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) , vol.16 , pp. 281-330
    • Marino, A.1    Saccon, C.2    Tosques, M.3
  • 65
    • 0043241101 scopus 로고    scopus 로고
    • Gradient flows on nonpositively curved metric spaces and harmonic maps
    • Mayer U.F. Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom. 6 (1998) 199-253
    • (1998) Comm. Anal. Geom. , vol.6 , pp. 199-253
    • Mayer, U.F.1
  • 66
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann R.J. A convexity principle for interacting gases. Adv. Math. 128 (1997) 153-179
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • McCann, R.J.1
  • 67
    • 0035618489 scopus 로고    scopus 로고
    • Polar factorization of maps on Riemannian manifolds
    • McCann R. 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.1
  • 68
    • 0034262838 scopus 로고    scopus 로고
    • Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric
    • Mikami T. Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric. Appl. Math. Optim. 42 (2000) 203-227
    • (2000) Appl. Math. Optim. , vol.42 , pp. 203-227
    • Mikami, T.1
  • 69
    • 0034373609 scopus 로고    scopus 로고
    • A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
    • Nochetto R.H., Savaré G., and Verdi C. A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. 53 (2000) 525-589
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 525-589
    • Nochetto, R.H.1    Savaré, G.2    Verdi, C.3
  • 71
    • 0032368806 scopus 로고    scopus 로고
    • Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
    • Otto F. Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory. Arch. Ration. Mech. Anal. 141 (1998) 63-103
    • (1998) Arch. Ration. Mech. Anal. , vol.141 , pp. 63-103
    • Otto, F.1
  • 72
    • 0007245075 scopus 로고    scopus 로고
    • Lubrication approximation with prescribed nonzero contact angle
    • Otto F. Lubrication approximation with prescribed nonzero contact angle. Comm. Partial Differential Equations 23 (1998) 2077-2164
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 2077-2164
    • Otto, F.1
  • 73
    • 0039525530 scopus 로고    scopus 로고
    • Evolution of microstructure in unstable porous media flow: A relaxational approach
    • Otto F. Evolution of microstructure in unstable porous media flow: A relaxational approach. Comm. Pure Appl. Math. 52 (1999) 873-915
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 873-915
    • Otto, F.1
  • 74
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • Otto F. The geometry of dissipative evolution equations: The porous medium equation. Comm. Partial Differential Equations 26 (2001) 101-174
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 75
    • 0001559554 scopus 로고    scopus 로고
    • Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
    • Otto F., and Villani C. Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173 (2000) 361-400
    • (2000) J. Funct. Anal. , vol.173 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 76
    • 33746121129 scopus 로고    scopus 로고
    • Eulerian calculus for the contraction in the Wasserstein distance
    • Otto F., and Westdickenberg M. Eulerian calculus for the contraction in the Wasserstein distance. SIAM J. Math. Anal. 37 (2005) 1227-1255
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 1227-1255
    • Otto, F.1    Westdickenberg, M.2
  • 78
    • 0001497003 scopus 로고
    • t - Δ φ{symbol}(u) = 0 with initial datum a measure
    • t - Δ φ{symbol}(u) = 0 with initial datum a measure. Nonlinear Anal. 6 (1982) 175-187
    • (1982) Nonlinear Anal. , vol.6 , pp. 175-187
    • Pierre, M.1
  • 79
    • 66049115176 scopus 로고    scopus 로고
    • On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation
    • to appear
    • A. Pratelli, On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation, Ann. Inst. H. Poincaré Probab. Statist., to appear.
    • Ann. Inst. H. Poincaré Probab. Statist
    • Pratelli, A.1
  • 81
    • 33745854790 scopus 로고    scopus 로고
    • Gradient flows of non convex functionals in Hilbert spaces and applications
    • Rossi R., and Savaré G. Gradient flows of non convex functionals in Hilbert spaces and applications. ESAIM Control Optim. Calc. Var. 12 (2006) 564-614
    • (2006) ESAIM Control Optim. Calc. Var. , vol.12 , pp. 564-614
    • Rossi, R.1    Savaré, G.2
  • 82
    • 0001779231 scopus 로고    scopus 로고
    • Error analysis for implicit approximations to solutions to Cauchy problems
    • Rulla J. Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal. 33 (1996) 68-87
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 68-87
    • Rulla, J.1
  • 83
  • 84
    • 33750193237 scopus 로고    scopus 로고
    • On the geometry of metric measure spaces
    • to appear
    • K. Sturm, On the geometry of metric measure spaces, Acta Math., to appear.
    • Acta Math
    • Sturm, K.1
  • 85
    • 64049116701 scopus 로고    scopus 로고
    • Optimal transportation, dissipative PDE's and functional inequalities
    • Martina Franca
    • Villani C. Optimal transportation, dissipative PDE's and functional inequalities. Optimal Transportation and Applications (2001), Martina Franca
    • (2001) Optimal Transportation and Applications
    • Villani, C.1
  • 86
    • 0004034109 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • Villani C. Lecture Notes in Math. Vol. 1813 (2003), Springer-Verlag, Berlin 53-89
    • (2003) Lecture Notes in Math. , vol.1813 , pp. 53-89
    • Villani, C.1
  • 87
    • 1542342359 scopus 로고    scopus 로고
    • Topics in Optimal Transportation
    • Amer. Math. Soc., Providence, RI
    • Villani C. Topics in Optimal Transportation. Grad. Stud. Math. Vol. 58 (2003), Amer. Math. Soc., Providence, RI
    • (2003) Grad. Stud. Math. , vol.58
    • Villani, C.1


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