Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 9
Number of page(s) 38
DOI https://doi.org/10.1051/cocv/2022089
Published online 19 January 2023
  1. Y. Achdou, F. Camilli, A. Cutrì and N. Tchou, Hamilton-Jacobi equations constrained on networks. Nonlinear Differ. Equ. Appl. 20 (2013) 413–445. [CrossRef] [Google Scholar]
  2. J.-P. Aubin and A. Cellina, Vol. 264 of Differential inclusions: set-valued maps and viability theory. Springer Science & Business Media (2012). [Google Scholar]
  3. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Springer Science & Business Media (2008). [Google Scholar]
  4. G. Barles, Solutions de viscosite des equations de Hamilton-Jacobi. Collection SMAI (1994). [Google Scholar]
  5. G. Barles, A. Briani and E. Chasseigne, A Bellman approach for two-domains optimal control problems in ℝn. ESAIM: COCV 19 (2013) 710–739. [CrossRef] [EDP Sciences] [Google Scholar]
  6. G. Barles, A. Briani and E. Chasseigne, A Bellman approach for regional optimal control problems in ℝn. SIAM J. Control Optim. 52 (2014) 1712–1744. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Barles and E. Chasseigne, (almost) everything you always wanted to know about deterministic control problems in stratified domains. Netw. Heter. Media 10 (2015) 809–836 and Corrigendum to “(Almost) everything you always wanted to know about deterministic control problems in stratified domains. Netw. Heter. Media 13 (2018) 373-378. [CrossRef] [Google Scholar]
  8. G. Barles and E. Chasseigne, An illustrated guide of the modern approches of Hamilton-Jacobi equations and control problems with discontinuities. Preprint arXiv:1812.09197 (2018). [Google Scholar]
  9. G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymp. Anal. 4 (1991) 271–283. [Google Scholar]
  10. R.C. Barnard and P.R. Wolenski, Flow invariance on stratified domains. Set-Valued Variat. Anal. 21 (2013) 377–403. [CrossRef] [Google Scholar]
  11. A. Bressan and Y. Hong, Optimal control problems on stratified domains. Netw. Heterog. Media 2 (2007) 313–331 and Errata corrige: Optimal control problems on stratified domains. Netw. Heterog. Media 8 (2013) 625. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Camilli and C. Marchi, A comparison among various notions ofviscosity solution for Hamilton-Jacobi equations on networks. J. Math. Anal. Appl. 407 (2013) 112–118. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Clarke, Vol. 264 of Functional analysis, calculus of variations and optimal control. Springer Science & Business Media (2013). [Google Scholar]
  14. F.H. Clarke, Vol. 5 of Optimization and nonsmooth analysis. Siam (1990). [Google Scholar]
  15. F.H. Clarke, Y.S. Ledyaev, R.J. Stern and P.R. Wolenski, Vol. 178 of Nonsmooth analysis and control theory. Springer Science & Business Media (2008). [Google Scholar]
  16. F.H. Clarke, R. Stern and P. Wolenski, Proximal smoothness and the lower-C2 property. J. Convex Anal. 2 (1995) 117–144. [MathSciNet] [Google Scholar]
  17. M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27 (1992) 1–67. [Google Scholar]
  18. M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American mathematical society, 277 (1983) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  19. L.C. Evans, Partial Differential Equations, Graduate studies in mathematics, vol. 19, American Mathematical Society, 1998. [Google Scholar]
  20. D. Ghilli, Z. Rao and H. Zidani, Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions. ESAIM: COCV (2017). https://doi.org/10.1051/cocv/2018072. [Google Scholar]
  21. J. Guerand and M. Koumaiha, Error estimates for a finite difference scheme associated with Hamilton-Jacobi equations on a junction. Numer. Math. 142 (2019) 525–575. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Hermosilla, R. Vinter and H. Zidani, Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints. Syst. Control Lett. 109 (2017) 30–36. [CrossRef] [Google Scholar]
  23. C. Hermosilla, P.R. Wolenski and H. Zidani, The Mayer and minimum time problems with stratified state constraints. Set-Valued Variat. Anal. 26 (2018) 643–662. [CrossRef] [Google Scholar]
  24. C. Hermosilla and H. Zidani, Infinite horizon problems on stratifiable state-constraints sets. J. Differ. Equ. 258 (2015) 1430–1460. [CrossRef] [Google Scholar]
  25. C. Imbert and R. Monneau, Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks. Annales scientifiques de l’ENS 50 (2017) 357–448 [Google Scholar]
  26. C. Imbert, R. Monneau and H. Zidani, A Hamilton-Jacobi approach to junction problems and application to traffic flows. ESAIM: COCV 19 (2013) 129–166. [CrossRef] [EDP Sciences] [Google Scholar]
  27. H. Ishii, A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 16 (1989) 105–135. [Google Scholar]
  28. A. Lechicki and A. Spakowski, A note on intersection of lower semicontinuous multifunctions. Proc. Am,. Math. Soc. 95 (1985) 119–122. [CrossRef] [Google Scholar]
  29. P.-L. Lions and P. Souganidis, Well posedness for multi-dimensional junction problems with Kirchoff-type conditions. Rendiconti Lincei - Matematica e Applicazioni 28 (2017) https://doi.org/10.4171/RLM/786. [Google Scholar]
  30. P.S. Morfe, Convergence and rates for Hamilton-Jacobi equations with Kirchoff junction conditions. Nonlinear Differ. Equ. Appl. 27 (2020) 1–69. [CrossRef] [Google Scholar]
  31. Z. Rao, A. Siconolfi and H. Zidani, Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations. J. Differ. Equ. 257 (2014) 3978–4014. [CrossRef] [Google Scholar]
  32. Z. Rao and H. Zidani, Hamilton-Jacobi-Bellman equations on multi-domains, in Control and Optimization with PDE Constraints. Springer (2013), pp. 93–116. [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.