Free access
Volume 13, Number 3, July-September 2007
Page(s) 484 - 502
Published online 05 June 2007
  1. O. Alvarez, Bounded-from-below viscosity solutions of Hamilton-Jacobi equations. Differential Integral Equations 10 (1997) 419–436. [MathSciNet]
  2. H. Attouch, Variational convergence for functions and operators. Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, MA (1984).
  3. M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997).
  4. M. Bardi and F. Da Lio, On the Bellman equation for some unbounded control problems. NoDEA 4 (1997) 491–510. [CrossRef] [MathSciNet]
  5. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Paris (1994).
  6. E.N. Barron and R. Jensen, Generalized viscosity solutions for Hamilton-Jacobi equations with time-measurable Hamiltonians. J. Differential Equations 68 (1987) 10–21. [CrossRef] [MathSciNet]
  7. E.N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex hamiltonians. Commun. Partial Differ. Equ. 15 (1990) 1713–1742.
  8. A. Bellaiche and J.-J. Risler, Sub-Riemannian geometry, Progress in Mathematics 144, Birkhäuser Verlag, Basel (1996).
  9. A. Bensoussan, Stochastic control by functional analysis methods, Studies in Mathematics and its Applications 11, North-Holland Publishing Co., Amsterdam (1982)
  10. I. Birindelli and J. Wigniolle, Homogenization of Hamilton-Jacobi equations in the Heisenberg group. Commun. Pure Appl. Anal. 2 (2003) 461–479. [CrossRef] [MathSciNet]
  11. R.W. Brockett, Control theory and singular Riemannian geometry, in: New Directions in Applied Mathematics (Cleveland, Ohio, 1980) Springer, New York-Berlin (1982) 11–27.
  12. R.W. Brockett, Pattern generation and the control of nonlinear systems. IEEE Trans. Automatic Control 48 (2003) 1699–1711. [CrossRef]
  13. P. Cannarsa and G. Da Prato, Nonlinear optimal control with infinite horizon for distributed parameter systems and stationary Hamilton-Jacobi equations. SIAM J. Control Optim. 27 (1989) 861–875. [CrossRef] [MathSciNet]
  14. I. Capuzzo Dolcetta, The Hopf solution of Hamilton-Jacobi equations. Elliptic and parabolic problems (Rolduc/Gaeta) (2001) 343–351.
  15. I. Capuzzo Dolcetta, Representations of solutions of Hamilton-Jacobi equations. Progr. Nonlinear Differential Equations Appl. 54 (2003) 79–90.
  16. I. Capuzzo Dolcetta and H. Ishii, Hopf formulas for state-dependent Hamilton-Jacobi equations. Preprint.
  17. A. Cutrì, Problemi semilineari ed integro-differenziali per sublaplaciani. Ph.D. Thesis, Universitá di Roma Tor Vergata (1997).
  18. F. Da Lio and O. Ley, Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications, Quaderno 8, Dipartimento di Matematica, Università di Torino (2004).
  19. F. Da Lio and W.M. McEneaney, Finite time-horizon risk-sensitive control and the robust limit under a quadratic growth assumption. SIAM J. Control Optim 40 (2002) 1628–1661 (electronic). [CrossRef] [MathSciNet]
  20. C.L. Fefferman and D.H. Phong, Subelliptic eigenvalue problems, in Conference on Harmonic Analysis in Honor of A. Zygmund, Wadsworth Math. Series 2 (1983) 590–606 .
  21. L. Hörmander, Hypoelliptic second order differential equations. Acta Math. 119 (1967) 147–171. [CrossRef] [MathSciNet]
  22. H. Ishii, Perron's method for Hamilton-Jacobi equations. Duke Math. J. 55 (1987) 369–384. [CrossRef] [MathSciNet]
  23. H. Ishii, Comparison results for Hamilton-Jacobi equations without growth condition on solutions from above. Appl. Anal. 67 (1997) 357–372. [CrossRef] [MathSciNet]
  24. D. Jerison and A. Sànchez-Calle, Subelliptic second order differential operator. Lect. Notes Math. Berlin-Heidelberg-New York 1277 (1987) 46–77.
  25. J.J. Manfredi and B. Stroffolini, A version of the Hopf-Lax formula in the Heisenberg group. Comm. Partial Differ. Equ. 27 (2002) 1139–1159. [CrossRef]
  26. R. Monti and F. Serra Cassano, Surface measures in Carnot Caratheodory spaces. Calc. Var. Partial Differ. Equ. 13 (2001) 339–376. [CrossRef]
  27. A. Nagel, E.M. Stein and S. Wainger, Balls and metrics defined by vector fields. I: Basic properties. Acta Math. 155 (1985) 103–147. [CrossRef] [MathSciNet]
  28. F. Rampazzo and C. Sartori, Hamilton-Jacobi-Bellman equations with fast gradient-dependence. Indiana Univ. Math. J. 49 (2000) 1043–1077. [CrossRef] [MathSciNet]
  29. F. Rampazzo and H. Sussmann, Set-valued differentials and a nonsmooth version of Chow's theorem, in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida (IEEE Publications, New York, 2001) 3 (2001) 2613–2618.
  30. B. Stroffolini, Homogenization of Hamilton-Jacobi Equations in Carnot Groups. ESAIM: COCV 13 (2007) 107–119. [CrossRef] [EDP Sciences]
  31. H.J. Sussmann, A general theorem on local controllability. SIAM J. Control. Optim. 25 (1987) 158–194. [CrossRef] [MathSciNet]