Free Access

This article has an erratum: []

Volume 21, Number 3, July-September 2015
Page(s) 876 - 899
Published online 20 May 2015
  1. Y. Achdou, F. Camilli, A. Cutrì and N. Tchou, Hamilton–Jacobi equations constrained on networks. Nonlinear Differ. Eq. Appl. 20 (2013) 413–445. [Google Scholar]
  2. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. With appendices by Maurizio Falcone and Pierpaolo Soravia. Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA (1997). [Google Scholar]
  3. 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]
  4. 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]
  5. G. Barles and B. Perthame, Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations. Appl. Math. Optim. 21 (1990) 21–44. [CrossRef] [MathSciNet] [Google Scholar]
  6. A.-P. Blanc, Deterministic exit time control problems with discontinuous exit costs. SIAM J. Control Optim. 35 (1997) 399–434. [CrossRef] [MathSciNet] [Google Scholar]
  7. A.-P. Blanc, Comparison principle for the Cauchy problem for Hamilton-Jacobi equations with discontinuous data. Nonlinear Anal. 45 (2001) 1015–1037. [CrossRef] [MathSciNet] [Google Scholar]
  8. I. Capuzzo-Dolcetta and P.-L. Lions, Hamilton-Jacobi equations with state constraints. Trans. Amer. Math. Soc. 318 (1990) 643–683. [Google Scholar]
  9. K.-J. Engel, M. Kramar Fijavž, R. Nagel and E. Sikolya, Vertex control of flows in networks. Netw. Heterog. Media 3 (2008) 709–722. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Frankowska and S. Plaskacz, Hamilton-Jacobi equations for infinite horizon control problems with state constraints, Calculus of variations and optimal control (Haifa, 1998). In vol. 411 of Res. Notes Math. Chapman & Hall/CRC, Boca Raton, FL (2000) 97–116. [Google Scholar]
  11. H. Frankowska and S. Plaskacz, Semicontinuous solutions of Hamilton-Jacobi-Bellman equations with degenerate state constraints. J. Math. Anal. Appl. 251 (2000) 818–838. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Garavello and B. Piccoli, Traffic flow on networks. Conservation laws models. In vol. of AIMS Ser. Appl. Math. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2006). [Google Scholar]
  13. C. Imbert and R. Monneau, The vertex test function for Hamilton-Jacobi equations on networks. Preprint arXiv:1306.2428 (2013). [Google Scholar]
  14. 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]
  15. H. Ishii, A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton–Jacobi equations. Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications. In vol. 2074 of Lect. Notes Math. Springer (2013) 111–249. [Google Scholar]
  16. H. Ishii and S. Koike, A new formulation of state constraint problems for first-order PDEs. SIAM J. Control Optim. 34 (1996) 554–571. [CrossRef] [MathSciNet] [Google Scholar]
  17. E.J. McShane and R.B. Warfield Jr., On Filippov’s implicit functions lemma. Proc. Amer. Math. Soc. 18 (1967) 41–47. [MathSciNet] [Google Scholar]
  18. S. Oudet, Hamilton–Jacobi equations for optimal control on heterogeneous structures with geometric singularity, work in progress (2014). [Google Scholar]
  19. Z. Rao, A. Siconolfi and H. Zidani, Transmission conditions on interfaces for Hamilton-Jacobi-bellman equations (2013). [Google Scholar]
  20. Z. Rao and H. Zidani, Hamilton–jacobi–bellman equations on multi-domains, Control and Optimization with PDE Constraints. Springer (2013) 93–116. [Google Scholar]
  21. D. Schieborn and F. Camilli, Viscosity solutions of Eikonal equations on topological networks. Calc. Var. Partial Differ. Eq. 46 (2013) 671–686. [CrossRef] [Google Scholar]
  22. H.M. Soner, Optimal control with state-space constraint. I. SIAM J. Control Optim. 24 (1986) 552–561. [Google Scholar]
  23. H.M. Soner, Optimal control with state-space constraint. II, SIAM J. Control Optim. 24 (1986) 1110–1122. [Google Scholar]
  24. M. Valadier, Sous-différentiels d’une borne supérieure et d’une somme continue de fonctions convexes. C. R. Acad. Sci. Paris Sér. A-B 268 (1969) A39–A42. [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.