EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 2 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 2
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2025087
Published online 23 January 2026
  1. L. Ambrosio, N. Gigli and G. Savaré, Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case, in Analysis and Numerics of Partial Differential Equations, Vol. 4 of Springer INdAM Series. Springer, Milan (2013) 63–115. [Google Scholar]
  2. C. Villani, Optimal transport. Vol. 338 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (2009). Old and new. [Google Scholar]
  3. P. Cardaliaguet, Notes on mean field games (from P.-L. Lions' lectures at college de france). https://www.ceremade.dauphine.fr/~cardaliaguet/MFG20130420.pdf (2013). [Google Scholar]
  4. C. Imbert, R. Monneau and H. Zidani, A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM Control Optim. Calc. Var. 19 (2013) 129–166. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  5. Y. Achdou, F. Camilli, A. Cutri, and N. Tchou, Hamilton-Jacobi equations constrained on networks. NoDEA Nonlinear Diff. Equ. Appl. 20 (2013) 413–445. [Google Scholar]
  6. C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks. Ann. Sci. Ec. Norm. Super. 50 (2017) 357–448. [Google Scholar]
  7. C. Imbert and R. Monneau, Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case. Discrete Contin. Dyn. Syst. 37 (2017) 6405–6435. [CrossRef] [MathSciNet] [Google Scholar]
  8. M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications. Birkhäuser Boston Inc., Boston, MA (1997). With appendices by Maurizio Falcone and Pierpaolo Soravia. [Google Scholar]
  10. S. Koike, A beginner's guide to the theory of viscosity solutions. Vol. 13 of MSJ Memoirs. Mathematical Society of Japan, Tokyo (2004). [Google Scholar]
  11. H.V. Tran, Hamilton-Jacobi equations - theory and applications. Graduate Studies in Mathematics, Vol. 213. American Mathematical Society, Providence, RI (2021). [Google Scholar]
  12. J.J. Manfredi and B. Stroffolini, A version of the Hopf-Lax formula in the Heisenberg group. Commun. Pari. Diff. Equ. 27 (2002) 1139–1159. [Google Scholar]
  13. F. Dragoni, Metric Hopf-Lax formula with semicontinuous data. Discrete Contin. Dyn. Syst. 17 (2007) 713–729. [Google Scholar]
  14. Y. Giga, N. Hamamuki and A. Nakayasu, Eikonal equations in metric spaces. Trans. Amer. Math. Soc. 367 (2015) 49–66. [Google Scholar]
  15. A. Nakayasu, Metric viscosity solutions for Hamilton-Jacobi equations of evolution type. Adv. Math. Sci. Appl. 24 (2014) 333–351. [Google Scholar]
  16. L. Ambrosio and J. Feng, On a class of first order Hamilton-Jacobi equations in metric spaces. J. Diff. Equ. 256 (2014) 2194–2245. [Google Scholar]
  17. W. Gangbo and A. Swiech, Optimal transport and large number of particles. Discrete Contin. Dyn. Syst. 34 (2014) 1397–1441. [Google Scholar]
  18. W. Gangbo and A. Swiech, Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes. Calc. Var. Part. Diff. Equ. 54 (2015) 1183–1218. [Google Scholar]
  19. A. Nakayasu and T. Namba, Stability properties and large time behavior of viscosity solutions of Hamilton-Jacobi equations on metric spaces. Nonlinearity 31 (2018) 5147–5161. [Google Scholar]
  20. S. Makida, Stability of viscosity solutions on expanding networks. Preprint (2023). [Google Scholar]
  21. S. Makida and A. Nakayasu, Stability of metric viscosity solutions under Hausdorff convergence. Preprint (2023). [Google Scholar]
  22. Q. Liu and A. Nakayasu, Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces. Discrete Contin. Dyn. Syst. 39 (2019) 157–183. [Google Scholar]
  23. Q. Liu, N. Shanmugalingam and X. Zhou, Equivalence of solutions of eikonal equation in metric spaces. J. Diff. Equ. 272 (2021) 979–1014. [Google Scholar]
  24. A. Daniilidis and D. Salas. A determination theorem in terms of the metric slope. Proc. Amer. Math. Soc. 150 (2022) 4325–4333. [Google Scholar]
  25. A. Daniilidis, T.M. Le and D. Salas, Metric compatibility and determination in complete metric spaces. Math. Z. 308 (2024) Paper No. 62, 31. [Google Scholar]
  26. R.T. Newcomb II, and J. Su, Eikonal equations with discontinuities. Diff. Integral Equ. 8 (1995) 1947–1960. [Google Scholar]
  27. F. Camilli and A. Siconolfi, Hamilton-Jacobi equations with measurable dependence on the state variable. Adv. Diff. Equ. 8 (2003) 733–768. [Google Scholar]
  28. A. Briani and A. Davini, Monge solutions for discontinuous Hamiltonians. ESAIM Control Optim. Calc. Var. 11 (2005) 229–251. [Google Scholar]
  29. F. Essebei, G. Giovannardi and S. Verzellesi, Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups, NoDEA Nonlinear Diff. Equ. Appl. 31 (2024) Paper No. 95. [Google Scholar]
  30. Q. Liu, N. Shanmugalingam and X. Zhou, Discontinuous eikonal equations in metric measure spaces. Trans. Amer. Math. Soc. 378 (2025) 695–729. [Google Scholar]
  31. Q. Liu and A. Mitsuishi, Principal eigenvalue problem for infinity Laplacian in metric spaces. Adv. Nonlinear Stud. 22 (2022) 548–573. [Google Scholar]
  32. W. Gangbo, T. Nguyen and A. Tudorascu, Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 15 (2008) 155–183. [Google Scholar]
  33. F. Camilli, D. Schieborn and C. Marchi, Eikonal equations on ramified spaces. Interfaces Free Bound. 15 (2013) 121–140. [Google Scholar]
  34. R. Hynd and H.K. Kim, Value functions in the Wasserstein spaces: finite time horizons. J. Funct. Anal. 269 (2015) 968–997. [Google Scholar]
  35. W. Gangbo, C. Mou and A. Swiech, Well-posedness for Hamilton-Jacobi equations on the Wasserstein space on graphs. Calc. Var. Part. Diff. Equ. 63 (2024) Paper No. 160, 41. [Google Scholar]
  36. O. Jerhaoui and H. Zidani, Viscosity solutions of Hamilton-Jacobi equations in proper CAT(0) spaces. J. Geom. Anal. 34 (2024) Paper No. 47, 53. [Google Scholar]
  37. F. Camilli, An Hopf-Lax formula for a class of measurable Hamilton-Jacobi equations. Nonlinear Anal. 57 (2004) 265–286. [Google Scholar]
  38. F. Camilli and A. Siconolfi, Time-dependent measurable Hamilton-Jacobi equations. Commun. Part. Diff. Equ. 30 (2005) 813–847. [Google Scholar]
  39. A. Davini, Bolza problems with discontinuous Lagrangians and Lipschitz-continuity of the value function. SIAM J. Control Optim. 46 (2007) 1897–1921. [Google Scholar]
  40. X. Chen and B. Hu, Viscosity solutions of discontinuous Hamilton-Jacobi equations. Interfaces Free Bound. 10 (2008) 339–359. [Google Scholar]
  41. Y. Giga and N. Hamamuki, Hamilton-Jacobi equations with discontinuous source terms. Commun. Part. Diff. Equ. 38 (2013) 199–243. [Google Scholar]
  42. I. Ekeland. On the variational principle. J. Math. Anal. Appl. 47 (1974) 324–353. [Google Scholar]
  43. I. Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc. (N.S.) 1 (1979) 443–474. [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.