Free Access
Issue
ESAIM: COCV
Volume 25, 2019
Article Number 78
Number of page(s) 36
DOI https://doi.org/10.1051/cocv/2018052
Published online 05 December 2019
  1. L. Ambrosio and W. Gangbo, Hamiltonian ODEs in the Wasserstein space of probability measures. Commun. Pure Appl. Math. 61 (2008) 18–53. [Google Scholar]
  2. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd edition. Lectures in Mathematics ETH Zürich. Birkhaüser Verlag, Basel (2008). [Google Scholar]
  3. G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Vol. 207 of Pitman Research Notes in Mathematics Series. Longman Scientific & Technical, Harlow (1989). [Google Scholar]
  4. P. Cardaliaguet, Notes on Mean-Field Games, Lectures by P.L. Lions. Collège de France (2010). [Google Scholar]
  5. P. Cardaliaguet, F. Delarue, J.-M. Lasry and P.-L. Lions, The master equation and the convergence problem in mean field games. Preprint arXiv:1509.02505 (2015). [Google Scholar]
  6. Y. Chen, W. Gangbo, T.T. Georgiou and A. Tannenbaum, On the Matrix Monge-Kantorovich Problem. Preprint arXiv:1701.02826 [math] (2017). [Google Scholar]
  7. S.-N. Chow, W. Huang, Y. Li and H. Zhou, Fokker–Planck equations for a free energy functional or Markov process on a graph. Arch. Ration. Mech. Anal. 203 (2012) 969–1008. [Google Scholar]
  8. S.-N Chow, W. Li and H. Zhou, Entropy dissipation of Fokker–Planck equations on graphs. Discrete Contin. Dyn. Syst. 38 (2018) 4929–4950. [CrossRef] [Google Scholar]
  9. S.-N. Chow, W. Li and H. Zhou, A discrete Schrödinger equation via optimal transport on graphs. Preprint arXiv:1705.07583 [math] (2017). [Google Scholar]
  10. I. Ekeland and R. Témam, Convex Analysis and Variational Problems. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA (1999). [Google Scholar]
  11. L.C. Evans and W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem. Mem. AMS 137 (1999) 1–66. [Google Scholar]
  12. W. Gangbo, An elementary proof of the polar decomposition of vector-valued functions. Arch. Ration. Mech. Anal. 128 (1995) 380–399. [Google Scholar]
  13. W. Gangbo and R. McCann, Optimal maps in Monge’s mass transport problem. C.R. Acad. Sci. Paris 321 (1995) 1653–1658. [Google Scholar]
  14. W. Gangbo and R. McCann, The geometry of optimal transport. Acta Math. 177 (1996) 113–161. [CrossRef] [MathSciNet] [Google Scholar]
  15. W. Gangbo, T. Nguyen and A. Tudorascu, Hamilton-Jacobi equations in the Wasserstein space. Meth. Appl. Anal. 15 (2008) 155–184. [Google Scholar]
  16. W. Gangbo and A. Swiech, Existence of a solution to an equation arising from the theory of Mean Field Games. J. Differ. Equ. 259 (2015) 6573–6643. [Google Scholar]
  17. W. Gangbo and A. Swiech, Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes. Calc. Var. Partial Differ. Equ. 54 (2015) 1183–1218. [Google Scholar]
  18. W. Gangbo and A. Tudorascu, Lagrangian dynamics on an infinite-dimensional torus; a Weak KAM theorem. Adv. Math. 224 (2010) 260–292. [CrossRef] [Google Scholar]
  19. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Maas, Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 (2011) 2250–2292. [Google Scholar]
  21. J.-F. Mertens, S. Sorin and S. Zamir, Repeated games. Vol. 55 of Econometric Society Monographs. Cambridge University Press, New York, 2015. [Google Scholar]
  22. A. Mielke, A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems. Nonlinearity 24 (2011) 1329–1346. [Google Scholar]
  23. Y. Shu, Hamilton-Jacobi equations on graph and applications. Potential Anal. 48 (2018) 125–157. [CrossRef] [Google Scholar]
  24. C. Villani, Topics in optimal transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2003. [CrossRef] [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.