Chinese Annals of Mathematics, Series B

, Volume 38, Issue 2, pp 379–392 | Cite as

New identities for Weak KAM theory



This paper records for the Hamiltonian H = 1/2 |p|2 + W(x) some old and new identities relevant for the PDE/variational approach to weak KAM theory.


Weak KAM theory Effective Hamiltonian Hamiltonian dynamics 

2000 MR Subject Classification

37J40 35A15 


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The author would like to thank the referees for very careful reading.


  1. [1]
    Bernardi, O., Cardin, F. and Guzzo, M., New estimates for Evans’ variational approach to weak KAM theory, Comm. in Contemporary Math., 15, 2013, 1250055.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Evans, L. C., Some new PDE methods for weak KAM theory, Calculus of Variations and Partial Differential Equations, 17, 2003, 159–177.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Evans, L. C., Further PDE methods for weak KAM theory, Calculus of Variations and Partial Differential Equations, 35, 2009, 435–462.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Evans, L. C. and Gomes, D., Effective Hamiltonians and averaging for Hamiltonian dynamics I, Archive Rational Mech. and Analysis, 157, 2001, 1–33.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Fathi, A., Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris Sr. I Math., 324, 1997, 1043–1046.CrossRefGoogle Scholar
  6. [6]
    Fathi, A., Weak KAM theorem in Lagrangian dynamics, Cambridge Studies in Advanced Mathematics, to be published.Google Scholar
  7. [7]
    Gomes, D., Iturriaga, R., Sanchez-Morgado, H. and Yu, Y., Mather measures selected by an approximation scheme, Proc. Amer. Math. Soc., 138, 2010, 3591–3601.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Gomes, D. and Sanchez-Morgado, H., A stochastic Evans-Aronsson problem, Trans. Amer. Math. Soc., 366, 2014, 903–929.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Lions, P.-L., Papanicolaou, G. and Varadhan, S. R. S., Homogenization of Hamilton–Jacobi equation, Comm. Pure Appl. Math., 56, 1987, 1501–1524.CrossRefGoogle Scholar
  10. [10]
    Mather, J., Minimal measures, Comment. Math. Helvetici, 64, 1989, 375–394.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Mather, J., Action minimizing invariant measures for positive definite Lagrangian systems, Math. Zeitschrift, 207, 1991, 169–207.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Yu, Y., L∞ variational problems and weak KAM theory, Comm. Pure Appl. Math., 60, 2007, 1111–1147.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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