Mather measures selected by an approximation scheme

Proceedings of the American Mathematical Society

Volumn 138, Issue 10, 2010, Pages 3591-3601

  Diogo, Gomes ^a   Iturriaga, Renato ^b   Sánchez Morgado, Héctor ^c   Yu, Yifeng ^d  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^c UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955605240     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-10-10361-X     Document Type: Article

References (18)

1. N. Anantharaman, On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics. J. Eur. Math. Soc. 6 (2004), no.2, 207-276. MR2055035 (2005i:82004)
2. N. Anantharaman, R. Iturriaga, P. Padilla, H. Sánchez-Morgado, Physical solutions of the Hamilton-Jacobi equation. Discrete Contin. Dyn. Syst. Ser. B 5 (2005), no.3, 513-528. MR2151719 (2006e:35031)
3. x F(x, f(x), f′(x)). Ark. Mat. 6 (1965), 33-53. MR0196551 (33:4738)
4. x F(x, f(x), f′(x)). II. Ark. Mat. 6 (1966), 409-431. MR0203541 (34:3391)
5. x F(x, f(x), f′(x)). III. Ark. Mat. 7 (1969), 509-512 (1969). MR0240690 (39:2035)
6. U. Bessi, Aubry-Mather theory and Hamilton-Jacobi equations. Comm. Math. Phys. 235 (2003), no.3, 495-511. MR1974512 (2004e:37096)
7. G. Contreras, R. Iturriaga, G. P. Paternain, M. Paternain, Lagrangian graphs, minimizing measures and Mañé's critical values. Geom. Funct. Anal. 8 (1998), no.5, 788-809. MR1650090 (99f:58075)
8. L. C. Evans, Some new PDE methods for weak KAM theory. Calc. Var. Partial Differential Equations 17 (2003), no.2, 159-177. MR1986317 (2004e:37097)
9. L. C. Evans, Towards a quantum analog of weak KAM theory. Comm. Math. Phys. 244 (2004), no.2, 311-334. MR2031033 (2005c:81063)
10. A. Fathi, Weak KAM theorem in Lagrangian dynamics, Cambridge University Press, in press.
11. D. Gomes, A stochastic analogue of Aubry-Mather theory. Nonlinearity 15 (2002), no.3, 581-603. MR1901094 (2003b:37096)
12. D. Gomes, Generalized Mather problem and selection principles for viscosity solutions and Mather measures. Adv. Calc. Var. 1 (2008), no.3, 291-307. MR2458239
13. H. R. Jauslin, H. O. Kreiss, J. Moser, On the forced Burgers equation with periodic boundary conditions. Differential Equations: La Pietra 1996. Proc. Symp. Pure Math. 65, Amer. Math. Soc., Providence, RI, 1999. MR1662751 (99m:35208)
14. P. L. Lions, G. Papanicolaou, S. R. S. Varadhan, Homogenization of Hamilton-Jacobi equations, unpublished manuscript, circa 1988.
15. J. N. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991), no.2, 169-207. MR1109661 (92m:58048)
16. Y. Yu, L∞ variational problems, Aronsson equations and weak KAM theory, Ph.D. dissertation, University of California, Berkeley, 2005.
17. 2 /2 Δ+V with a degenerate potential V. Proc. Amer. Math. Soc. 135 (2007), no.5, 1449-1454. MR2276654 (2007k:35079)
18. Y. Yu, L∞ variational problems and weak KAM theory. Comm. Pure Appl. Math. 60 (2007), no.8, 1111-1147. MR2330625 (2008f:49008)