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New identities for Weak KAM theory

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Abstract

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.

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References

  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.

    Article  MathSciNet  MATH  Google Scholar 

  2. Evans, L. C., Some new PDE methods for weak KAM theory, Calculus of Variations and Partial Differential Equations, 17, 2003, 159–177.

    Article  MathSciNet  MATH  Google Scholar 

  3. Evans, L. C., Further PDE methods for weak KAM theory, Calculus of Variations and Partial Differential Equations, 35, 2009, 435–462.

    Article  MathSciNet  MATH  Google Scholar 

  4. Evans, L. C. and Gomes, D., Effective Hamiltonians and averaging for Hamiltonian dynamics I, Archive Rational Mech. and Analysis, 157, 2001, 1–33.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  6. Fathi, A., Weak KAM theorem in Lagrangian dynamics, Cambridge Studies in Advanced Mathematics, to be published.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  8. Gomes, D. and Sanchez-Morgado, H., A stochastic Evans-Aronsson problem, Trans. Amer. Math. Soc., 366, 2014, 903–929.

    Article  MathSciNet  MATH  Google Scholar 

  9. Lions, P.-L., Papanicolaou, G. and Varadhan, S. R. S., Homogenization of Hamilton–Jacobi equation, Comm. Pure Appl. Math., 56, 1987, 1501–1524.

    Article  Google Scholar 

  10. Mather, J., Minimal measures, Comment. Math. Helvetici, 64, 1989, 375–394.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mather, J., Action minimizing invariant measures for positive definite Lagrangian systems, Math. Zeitschrift, 207, 1991, 169–207.

    Article  MathSciNet  MATH  Google Scholar 

  12. Yu, Y., L∞ variational problems and weak KAM theory, Comm. Pure Appl. Math., 60, 2007, 1111–1147.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, USA

    Lawrence Craig Evans

Authors
  1. Lawrence Craig Evans
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Correspondence to Lawrence Craig Evans.

Additional information

For Haim Brezis, in continuing admiration

This work was supported by NSF Grant DMS-1301661 and the Miller Institute for Basic Research in Science.

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Evans, L.C. New identities for Weak KAM theory. Chin. Ann. Math. Ser. B 38, 379–392 (2017). https://doi.org/10.1007/s11401-017-1074-9

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  • DOI: https://doi.org/10.1007/s11401-017-1074-9

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