Free Access
Issue
ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 795 - 815
DOI https://doi.org/10.1051/cocv:2006023
Published online 11 October 2006
  1. M. Bardi and L.C. Evans, On Hopf's formula for solutions of Hamilton-Jacobi equations. Nonlinear Anal. Th. Meth. Appl. 8 (1984) 1373–1381. [CrossRef] [Google Scholar]
  2. F. Cardin, On viscosity solutions and geometrical solutions of Hamilton-Jacobi equations. Nonlinear Anal. Th. Meth. Appl. 20 (1993) 713–719. [CrossRef] [Google Scholar]
  3. M. Chaperon, Lois de conservation et geometrie symplectique. C.R. Acad. Sci. Paris Ser. I Math., 312 (1991) 345–348. [Google Scholar]
  4. F.H. Clarke, Optimization and Nonsmooth Analysis. J. Wiley, New York (1983). [Google Scholar]
  5. M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 277 (1983) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  6. M.G. Crandall, L.C. Evans and P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 282 (1984) 487–502. [CrossRef] [MathSciNet] [Google Scholar]
  7. M.V. Day, On Lagrange manifolds and viscosity solutions. J. Math. Syst. Estim. Contr. 8 (1998) http://www.math.vt.edu/people/day/research/LMVS.pdf [Google Scholar]
  8. S.Yu. Dobrokhotov, V.N. Kolokoltsov and V.P. Maslov, Quantization of the Bellman equation, exponential asymptotics and tunneling, in Advances in Soviet Mathematics, V.P. Maslov and S.N. Samborskii, Eds., American Mathematical Society, Providence, Rhode Island 13 (1992) 1–46 . [Google Scholar]
  9. W.H Fleming and H.M. Soner, Controlled markov processes and viscosity solutions. Springer-Verlag, New York (1993). [Google Scholar]
  10. H. Frankowska, Hamilton-Jacobi equations: viscosity solutions and generalised gradients. J. Math. Anal. Appl. 141 (1989) 21–26. [CrossRef] [MathSciNet] [Google Scholar]
  11. E. Hopf, Generalized solutions of non-linear equations of first order. J. Math. Mech. 14 (1965) 951–973. [MathSciNet] [Google Scholar]
  12. T. Joukovskaia, Thèse de Doctorat, Université de Paris VII, Denis Diderot (1993). [Google Scholar]
  13. F. Laudenbach and J.C. Sikorav, Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibre cotangent. Invent. Math. 82 (1985) 349–357. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems. Applied Mathematical Sciences Series 74, Springer-Verlag, Berlin (1989). [Google Scholar]
  15. D. McCaffrey and S.P. Banks, Lagrangian Manifolds, Viscosity Solutions and Maslov Index. J. Convex Anal. 9 (2002) 185–224. [MathSciNet] [Google Scholar]
  16. D. McCaffrey, Viscosity Solutions on Lagrangian Manifolds and Connections with Tunnelling Operators, in Idempotent Mathematics and Mathematical Physics, V.P. Maslov and G.L. Litvinov Eds., Contemp. Math. 377, American Mathematical Society, Providence, Rhode Island (2005). [Google Scholar]
  17. D. McCaffrey, Geometric existence theory for the control-affine Formula problem, to appear in J. Math. Anal & Appl. (August 2005). [Google Scholar]
  18. G.P. Paternain, L. Polterovich and K.F. Siburg, Boundary rigidity for Lagrangian submanifolds, non-removable intersections and Aubry-Mather theory. Moscow Math. J. 3 (2003) 593–619. [Google Scholar]
  19. J.C. Sikorav, Sur les immersions lagrangiennes dans un fibre cotangent admettant une phase generatrice globale. C. R. Acad. Sci. Paris, Ser. I Math. 302 (1986) 119–122. [Google Scholar]
  20. P. Soravia, Formula control of nonlinear systems: differential games and viscosity solutions. SIAM J. Contr. Opt. 34 (1996) 1071–1097. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.J. van der Schaft, On a state space approach to nonlinear Formula control. Syst. Contr. Lett. 16 (1991) 1–8. [CrossRef] [Google Scholar]
  22. A.J. van der Schaft, L2 gain analysis of nonlinear systems and nonlinear state feedback Formula control. IEEE Trans. Automatic Control AC-37 (1992) 770–784. [Google Scholar]
  23. C. Viterbo, Symplectic topology as the geometry of generating functions. Math. Ann. 292 (1992) 685–710. [CrossRef] [MathSciNet] [Google Scholar]
  24. C. Viterbo, Solutions d'equations d'Hamilton-Jacobi et geometrie symplectique, Addendum to: Séminaire sur les équations aux Dérivés Partielles 1994–1995, École Polytech., Palaiseau (1996). [Google Scholar]
  25. A. Ottolengi and C. Viterbo, Solutions généralisées pour l'équation de Hamilton-Jacobi dans le cas d'évolution, unpublished. [Google Scholar]
  26. A. Weinstein, Lectures on symplectic manifolds, Regional Conference Series in Mathematics 29, Conference Board of the Mathematical Sciences, AMS, Providence, Rhode Island (1977). [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.