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Inventiones mathematicae

, Volume 155, Issue 2, pp 363–388 | Cite as

Existence of C1 critical subsolutions of the Hamilton-Jacobi equation

  • Albert Fathi
  • Antonio Siconolfi
Article

Keywords

Critical Subsolutions 
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References

  1. 1.
    Bangert, V.: Minimal measures and minimizing closed normal one-currents. Geom. Funct. Anal. 9, 413–427 (1999) CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Barles, G.: Solutions de viscosité des équations de Hamilton-Jacobi. Paris: Springer 1994 Google Scholar
  3. 3.
    Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Boston, MA: Birkhäuser Boston Inc. 1997 Google Scholar
  4. 4.
    Buttazzo, G., Giaquinta, M., Hildebrandt, S.: One-dimensional variational problems, An introduction. Oxford Lecture Series in Mathematics and its Applications, Vol. 15. Oxford: Oxford University Press 1998 Google Scholar
  5. 5.
    Clarke, F.H.: Optimization and Nonsmooth Analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts. New York: John Wiley & Sons 1983 Google Scholar
  6. 6.
    Contreras, G., Iturriaga, R., Paternain, G., Paternain, M.: Lagrangian graphs, minimizing measures and Mañé’s critical values. Geom. Funct. Anal. 8, 788–809 (1998) CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Contreras, G.: Action potential and weak KAM solutions. Calc. Var. Partial Differ. Equ. 13, 427–458 (2001) CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Dugundji, J.: Topology. Boston: Allyn and Bacon, Inc. 1970 Google Scholar
  9. 9.
    Fathi, A.: Weak KAM Theorem and Lagrangian Dynamics. Cambridge University Press 2004. To appear Google Scholar
  10. 10.
    Fathi, A.: Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci., Paris, Sér. I, Math. 324, 1043–1046 (1997) Google Scholar
  11. 11.
    Fathi, A.: Solutions KAM faibles conjuguées et barrières de Peierls. C. R. Acad. Sci., Paris, Sér. I, Math. 325, 649–652 (1997) Google Scholar
  12. 12.
    Fathi, A., Maderna, E.: Weak KAM theorem on non compact manifolds. To appear in NoDEA, Nonlinear Differ. Equ. Appl. Google Scholar
  13. 13.
    Gromov, M.: Metric structures for Riemannian and non-Riemannian spaces. Boston, MA: Birkhäuser Boston Inc. 1999 Google Scholar
  14. 14.
    Lions, P.L., Papanicolaou, G., Varadhan, S.R.S.: Homogenization of Hamilton-Jacobi equation. Unpublished preprint (1987) Google Scholar
  15. 15.
    Mañé, R.: Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity 9, 273–310 (1996) CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Mather, J.N.: Action minimizing measures for positive definite Lagrangian systems. Math. Z. 207, 169–207 (1991) MathSciNetzbMATHGoogle Scholar
  17. 17.
    Mather, J.N.: Variational construction of connecting orbits. Ann. Inst. Fourier 43, 1349–1386 (1993)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.DMI & UMPAEcole Normale SupérieureLyonFrance
  2. 2.Departimento di MatematicaUniv. ‘La Sapienza’RomaItaly

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