Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems

Calculus of Variations and Partial Differential Equations

Volumn 14, Issue 3, 2002, Pages 345-357

  Gomes, Diogo Aguiar ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b Departamento de Física   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036556944     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260100106     Document Type: Article

References (15)

1. V.I. Arnold. Mathematical methods of classical mechanics. New York: Springer, 1989. Translated from the 1974 original by K. Vogtmann and A. Weinstein.
2. A. Braides and A. Defranceschi. Homogenization of Multiple Integrals. Oxford Univ. Press, 1998.
3. M. Concordel. Periodic homogenization of Hamilton-Jacobi equations. PhD thesis, UC Berkeley, 1995.
4. Marie C. Concordel. Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalues und variational formula. Indiana Univ. Math. J., 45(4): 1095-1117, 1996.
5. Marie C. Concordel. Periodic homogenization of Hamilton-Jacobi equations. II. Eikonal equations. Proc. Roy. Soc. Edinburgh Sect. A, 127(4): 665-689, 1997.
6. E. Weinan. Aubry-Mather theory and periodic solutions of the forced Burgers equation. Comm. Pure Appl. Math., 52(7): 811-828, 1999.
7. L. C. Evans and D. Gomes. Effective Hamiltonians and averaging for Hamiltonian dynamicsI. Preprint, 1999.
8. Albert Fathi. Solutions KAM faibles conjuguées et barrières de Peierls. C. R. Acad. Sci. Pads Sér. I. Math., 325(6): 649-652, 1997.
9. Albert Fathi. Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci. Pads Sér. I. Math., 324(9): 1043-1046, 1997.
10. Albert Fathi. Orbite hétéroclines et ensemble de Peierls. C. R. Acad. Sci. Paris Sér. I. Math., 326: 1213-1216, 1998.
11. Albert Fathi. Sur la convergence du semi-groupe de Lax-Oleinik. C. R. Acad. Sci. Paris Sér. I. Math., 327: 267-270, 1998.
12. Wendell H. Fleming and H. Mete Soner. Controlled Markov processes and viscosity solutions. New York: Springer, 1993.
13. P. L. Lions, G. Papanicolaou, and S. R. S. Varadhan. Homogenization of Hamilton-Jacobi equations. Preliminary Version, 1988.
14. John N. Mather. Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z., 207(2): 169-207, 1991.
15. Ricardo Mañé. Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity, 9(2): 273-310, 1996.