Free Access
Volume 11, Number 4, October 2005
Page(s) 522 - 541
Published online 15 September 2005
  1. O. Alvarez and M. Bardi, A general convergence result for singular perturbations of fully nonlinear degenerate parabolic PDEs. University of Padova, Preprint (2002).
  2. O. Alvarez and M. Bardi, Singular perturbations of nonlinear degenerate parabolic PDEs: a general convergence result. Arch. Rational Mech. Anal. 170 (2003) 17–61. [CrossRef] [MathSciNet]
  3. M. Arisawa, Ergodic problem for the Hamilton-Jacobi-Bellman equation I. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 415–438. [CrossRef] [MathSciNet]
  4. M. Arisawa, Ergodic problem for the Hamilton-Jacobi-Bellman equation II. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 1–24. [CrossRef] [MathSciNet]
  5. M. Arisawa and P.L. Lions, Continuity of admissible trajectories for state constraints control problems. Discrete Cont. Dyn. Systems 2 (1996) 297–305. [CrossRef]
  6. M. Arisawa and P.L. Lions, On ergodic stochastic control. Commun. Partial Differ. Equations 23 (1998) 2187–2217.
  7. J.P. Aubin and A. Cellina, Differential inclusions. Set-valued maps and viability theory. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin 264 (1984) XIII+342.
  8. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of the Hamilton-Jacobi equations. Birkhäuser, Boston (1997).
  9. M. Bardi, S. Koike and P. Soravia, Pursuit-evasion game with state constraints: dynamic programming and discrete-time approximations. Discrete Cont. Dyn. Systems 6 (2000) 361–380. [CrossRef]
  10. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. (French) [Viscosity solutions of Hamilton-Jacobi equations.] Mathématiques & Applications [Mathematics & Applications]. Springer-Verlag, Paris 17 (1994) X+194.
  11. P. Bettiol, Weak Solutions in Hamilton-Jacobi and Control Theory. Ph.D. Thesis University of Padova (2002).
  12. P. Bettiol, P. Cardaliaguet and M. Quincampoix, Zero-sum state constrained Differential Games: Victory domains and Existence of value function for Bolza Problem. Preprint SISSA/ISAS Ref. 85/2004/M.
  13. I. Capuzzo-Dolcetta and P.L. Lions, Hamilton-Jacobi equations with state constraints. Trans. Amer. Math. Soc. 318 (1990) 643–687. [CrossRef] [MathSciNet]
  14. P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre, Pursuit differential games with state constraints. SIAM J. Control Optim. 39 (2001) 1615–1632. [CrossRef] [MathSciNet]
  15. P. Cardaliaguet and S. Plaskacz, Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians. SIAM J. Control Optim. 38 (2000) 1501–1520. [CrossRef] [MathSciNet]
  16. I.P. Cornfeld, S.V. Fomin and Ya.G. Sinaĭ, Ergodic theory. Springer-Verlag, New York (1982). X+486.
  17. M.G. Crandall and P.L. Lions, Condition d'unicité pour les solutions généralisées des équations de Hamilton-Jacobi du premier ordre. (French. English summary.) C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 183–186.
  18. M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. [CrossRef] [MathSciNet]
  19. M.G. Crandall, L.C. Evans and P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 282 (1984) 487–502. [CrossRef] [MathSciNet]
  20. L.C. Evans, Partial differential equations. Graduate Studies in Mathematics, 19 AMS, Rhodeisland (1998).
  21. L.C. Evans and H. Ishii, Differential games and nonlinear first order PDE on bounded domains. Manuscripta Math. 49 (1984) 109–139. [CrossRef] [MathSciNet]
  22. H. Federer, Curvature measures. Trans. Amer. Math. Soc. 93 (1959) 418–491. [CrossRef] [MathSciNet]
  23. H. Frankowska, S. Plaskacz and T. Rzeżuchowski, Measurable viability theorems and the Hamilton-Jacobi-Bellman equation. J. Differential Equations 116 (1995) 265–305. [CrossRef] [MathSciNet]
  24. H. Frankowska and F. Rampazzo, Filippov's and Filippov-Ważewski's theorems on closed domains. J. Differential Equations 161 (2000) 449–478. [CrossRef] [MathSciNet]
  25. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin (2001). XIV+517.
  26. H. Ishii, Lecture notes on viscosity solutions. Brown University, Providence, RI (1988).
  27. S. Koike, On the state constraint problem for differential games. Indiana Univ. Math. J. 44 (1995) 467–487. [MathSciNet]
  28. P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, Mass.-London 69 (1982) IV+317.
  29. P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications. Comm. Partial Differ. Equ. 8 (1983) 1101–1174. [CrossRef] [MathSciNet]
  30. P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations. Duke Math. J. 52 (1985), 793–820.
  31. P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984) 511–537. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  32. P. Loreti and M.E. Tessitore, Approximation and regularity results on constrained viscosity solutions of Hamilton-Jacobi-Bellman equations. J. Math. Systems Estim. Control 4 (1994) 467–483. [MathSciNet]
  33. B. Simon, Functional integration and quantum physics. Pure Appl. Math. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London 86 (1979) IX+296.
  34. M.H. Soner, Optimal control with state-space constraint. I. SIAM J. Control Optim. 24 (1986) 552–561. [CrossRef] [MathSciNet]

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.