Viscosity Solutions of Hamilton-jacobi Equations, and Asymptotics for Hamiltonian Systems

@inproceedings{Gomes2000ViscositySO,
  title={Viscosity Solutions of Hamilton-jacobi Equations, and Asymptotics for Hamiltonian Systems},
  author={Diogo A. Gomes},
  year={2000}
}
In this paper we apply the theory of viscosity solutions of Hamilton-Jacobi equations to understand the structure of certain Hamiltonian flows. In particular, we describe the asymptotic behavior of minimizing orbits of Hamiltonian flows by proving a weak KAM theorem which holds under very general conditions. Then, using Mather measures, we prove results on the uniform continuity, difference quotients and non-uniqueness of solutions of time-independent Hamilton-Jacobi equations. 
Highly Cited
This paper has 20 citations. REVIEW CITATIONS
15 Citations
14 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 14 references

Homogenization of multiple integrals

  • Andrea Braides, Anneliese Defranceschi
  • 1998

Orbite hétéroclines et ensemble de Peierls

  • Albert Fathi
  • C. R. Acad. Sci. Paris Sér. I Math.,
  • 1998

Sur la convergence du semi-groupe de Lax-Oleinik

  • Albert Fathi
  • C. R. Acad. Sci. Paris Sér. I Math.,
  • 1998

Periodic homogenisation of Hamilton-Jacobi equations. II

  • Marie C. Concordel
  • Eikonal equations. Proc. Roy. Soc. Edinburgh Sect…
  • 1997

Solutions KAM faibles conjuguées et barrières de Peierls

  • Albert Fathi
  • C. R. Acad. Sci. Paris Sér. I Math.,
  • 1997

Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens

  • Albert Fathi
  • C. R. Acad. Sci. Paris Sér. I Math.,
  • 1997

Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity

  • Ricardo Mañé
  • 1996

Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalues and variational formula

  • Marie C. Concordel
  • Indiana Univ. Math. J.,
  • 1996

Similar Papers

Loading similar papers…