Free Access
Issue
ESAIM: COCV
Volume 15, Number 3, July-September 2009
Page(s) 712 - 740
DOI https://doi.org/10.1051/cocv:2008044
Published online 19 July 2008
  1. M. Agueh, Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory. Adv. Differential Equations 10 (2005) 309–360. [MathSciNet] [Google Scholar]
  2. L. Ambrosio, Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19 (1995) 191–246. [MathSciNet] [Google Scholar]
  3. L. Ambrosio, Transport equation and cauchy problem for non-smooth vector fields. Lecture Notes of the CIME Summer school (2005) available on line at http://cvgmt.sns.it/people/ambrosio/. [Google Scholar]
  4. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000). [Google Scholar]
  5. L. Ambrosio, N. Gigli and G. Savarè, Gradient flows in metric spaces and in the Wasserstein spaces of probability measures. Birkhäuser (2005). [Google Scholar]
  6. A. Arnold, P. Markowich, G. Toscani and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Comm. Partial Diff. Eq. 26 (2001) 43–100. [CrossRef] [Google Scholar]
  7. J.D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [CrossRef] [MathSciNet] [Google Scholar]
  8. E.A. Carlen and W. Gangbo, Constrained steepest descent in the 2-Wasserstein metric. Ann. Math. 157 (2003) 807–846. [CrossRef] [Google Scholar]
  9. E.A. Carlen and W. Gangbo, Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric. Arch. Rational Mech. Anal. 172 (2004) 21–64. [CrossRef] [Google Scholar]
  10. J.A. Carrillo, A. Jüngel, P.A. Markowich, G. Toscani and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities. Monatsh. Math. 133 (2001) 1–82. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.A. Carrillo, R.J. McCann and C. Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19 (2003) 971–1018. [MathSciNet] [Google Scholar]
  12. J.A. Carrillo, R.J. McCann and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media. Arch. Rational Mech. Anal. 179 (2006) 217–263. [CrossRef] [Google Scholar]
  13. J. Crank, The mathematics of diffusion. Clarendon Press, Oxford, second edition (1975). [Google Scholar]
  14. G. De Cecco and G. Palmieri, Intrinsic distance on a Lipschitz Riemannian manifold. Rend. Sem. Mat. Univ. Politec. Torino 46 (1990) 157–170. [Google Scholar]
  15. G. De Cecco and G. Palmieri, Intrinsic distance on a LIP Finslerian manifold. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 17 (1993) 129–151. [Google Scholar]
  16. G. De Cecco and G. Palmieri, LIP manifolds: from metric to Finslerian structure. Math. Z. 218 (1995) 223–237. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. De Giorgi, New problems on minimizing movements, in Boundary value problems for partial differential equations and applications, RMA Res. Notes Appl. Math. 29, Masson, Paris (1993) 81–98. [Google Scholar]
  18. E. De Giorgi, A. Marino and M. Tosques, Problems of evolution in metric spaces and maximal decreasing curve. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 68 (1980) 180–187. [MathSciNet] [Google Scholar]
  19. M. Degiovanni, A. Marino and M. Tosques, Evolution equations with lack of convexity. Nonlinear Anal. 9 (1985) 1401–1443. [CrossRef] [MathSciNet] [Google Scholar]
  20. C. Dellacherie and P.A. Meyer, Probabilities and potential. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  21. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992). [Google Scholar]
  22. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  23. D. Kinderlehrer and A. Tudorascu, Transport via mass transportation. Discrete Contin. Dyn. Syst. Ser. B 6 (2006) 311–338. [MathSciNet] [Google Scholar]
  24. S. Lisini, Characterization of absolutely continuous curves in Wasserstein spaces. Calc. Var. Partial Differential Equations 28 (2007) 85–120. [CrossRef] [MathSciNet] [Google Scholar]
  25. R.J. McCann, A convexity principle for interacting gases. Adv. Math. 128 (1997) 153–179. [CrossRef] [MathSciNet] [Google Scholar]
  26. F. Otto, Doubly degenerate diffusion equations as steepest descent. Manuscript (1996) available on line at http://www-mathphys.iam.uni-bonn.de/web/forschung/publikationen/main-en.htm. [Google Scholar]
  27. F. Otto, Evolution of microstructure in unstable porous media flow: a relaxational approach. Comm. Pure Appl. Math. 52 (1999) 873–915. [CrossRef] [MathSciNet] [Google Scholar]
  28. F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Diff. Eq. 26 (2001) 101–174. [CrossRef] [MathSciNet] [Google Scholar]
  29. L. Petrelli and A. Tudorascu, Variational principle for general diffusion problems. Appl. Math. Optim. 50 (2004) 229–257. [CrossRef] [MathSciNet] [Google Scholar]
  30. K.-T. Sturm, Convex functionals of probability measures and nonlinear diffusions on manifolds. J. Math. Pures Appl. 84 (2005) 149–168. [CrossRef] [MathSciNet] [Google Scholar]
  31. J.L. Vázquez, The porous medium equation, Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, Oxford (2007). [Google Scholar]
  32. C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics 58. American Mathematical Society, Providence, RI (2003). [Google Scholar]
  33. M.-K. von Renesse and K.-T. Sturm, Transport inequalities, gradient estimates, entropy and Ricci curvature. Comm. Pure Appl. Math. 58 (2005) 923–940. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.