Skip to main content
SpringerLink
Log in

Existence of C1 critical subsolutions of the Hamilton-Jacobi equation

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bangert, V.: Minimal measures and minimizing closed normal one-currents. Geom. Funct. Anal. 9, 413–427 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barles, G.: Solutions de viscosité des équations de Hamilton-Jacobi. Paris: Springer 1994

  3. Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Boston, MA: Birkhäuser Boston Inc. 1997

  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

  5. Clarke, F.H.: Optimization and Nonsmooth Analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts. New York: John Wiley & Sons 1983

  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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Contreras, G.: Action potential and weak KAM solutions. Calc. Var. Partial Differ. Equ. 13, 427–458 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dugundji, J.: Topology. Boston: Allyn and Bacon, Inc. 1970

  9. Fathi, A.: Weak KAM Theorem and Lagrangian Dynamics. Cambridge University Press 2004. To appear

  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. 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. Fathi, A., Maderna, E.: Weak KAM theorem on non compact manifolds. To appear in NoDEA, Nonlinear Differ. Equ. Appl.

  13. Gromov, M.: Metric structures for Riemannian and non-Riemannian spaces. Boston, MA: Birkhäuser Boston Inc. 1999

  14. Lions, P.L., Papanicolaou, G., Varadhan, S.R.S.: Homogenization of Hamilton-Jacobi equation. Unpublished preprint (1987)

  15. Mañé, R.: Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity 9, 273–310 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mather, J.N.: Action minimizing measures for positive definite Lagrangian systems. Math. Z. 207, 169–207 (1991)

    MathSciNet  MATH  Google Scholar 

  17. Mather, J.N.: Variational construction of connecting orbits. Ann. Inst. Fourier 43, 1349–1386 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DMI & UMPA, Ecole Normale Supérieure, 26, allée d’Italie, 69364, Lyon, France

    Albert Fathi

  2. Departimento di Matematica, Univ. ‘La Sapienza’, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Antonio Siconolfi

Authors
  1. Albert Fathi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Siconolfi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Albert Fathi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fathi, A., Siconolfi, A. Existence of C1 critical subsolutions of the Hamilton-Jacobi equation. Invent. math. 155, 363–388 (2004). https://doi.org/10.1007/s00222-003-0323-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-003-0323-6

Keywords

Search

Navigation