Free access
Issue
ESAIM: COCV
Volume 15, Number 1, January-March 2009
Page(s) 1 - 48
DOI http://dx.doi.org/10.1051/cocv:2008017
Published online 23 January 2009
  1. G. Alberti, L. Ambrosio and X. Cabré, On a long standing conjecture of De Giorgi: symmetry in 3d for general nonlinearities and a local minimality property. Acta Appl. Math. 65 (2001) 9–33. [CrossRef] [MathSciNet]
  2. S. Aubry and P.Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions. Physica 8D (1983) 381–422.
  3. F. Auer and V. Bangert, Differentiability of the stable norm in codimension one. CRAS 333 (2001) 1095–1100.
  4. V. Bangert, On minimal laminations of the torus. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989) 95–138.
  5. V. Bangert, Geodesic rays, Busemann functions and monotone twist maps. Calc. Var. 2 (1994) 49–63. [CrossRef] [MathSciNet]
  6. P. Bernard and B. Buffoni, Optimal mass transportation and Mather theory. J. Eur. Math. Soc. 9 (2007) 85–121. [CrossRef] [MathSciNet]
  7. D. Burago, S. Ivanov and B. Kleiner, On the structure of the stable norm of periodic metrics. Math. Res. Lett. 4 (1997) 791–808. [MathSciNet]
  8. L. De Pascale, M.S. Gelli and L. Granieri, Minimal measures, one-dimensional currents and the Monge-Kantorovich probem. Calc. Var. Partial Differential Equations 27 (2006) 1–23. [CrossRef] [MathSciNet]
  9. K. Deimling, Nonlinear Functional Analysis. Springer, Berlin (1985).
  10. M.P. do Carmo, Differential Forms and Applications. Springer, Berlin (1994).
  11. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford (1980).
  12. D. Massart, Stable norms of surfaces: local structure of the unit ball at rational directions. GAFA 7 (1997) 996–1010. [CrossRef]
  13. D. Massart, On Aubry sets and Mather's action functional. Israel J. Math. 134 (2003) 157–171. [CrossRef] [MathSciNet]
  14. J.N. Mather, Differentiability of the minimal average action as a function of the rotation number. Bol. Soc. Bras. Mat. 21 (1990) 59–70. [CrossRef]
  15. J.N. Mather, Action minimizing invariant measures for positive-definite Lagrangian systems. Math. Zeit. 207 (1991) 169–207. [CrossRef] [MathSciNet]
  16. J.N. Mather, Variational construction of connecting orbits. Ann. Inst. Fourier 43 (1993) 1349–1386.
  17. J. Moser, Minimal solutions of variational problems on a torus. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1989) 229–272.
  18. O. Osuna, Vertices of Mather's beta function. Ergodic Theory Dynam. Systems 25 (2005) 949–955. [CrossRef] [MathSciNet]
  19. P.H. Rabinowitz and E. Stredulinsky, Mixed states for an Allen-Cahn type equation. Comm. Pure Appl. Math. 56 (2003) 1078–1134. [CrossRef] [MathSciNet]
  20. W. Senn, Strikte Konvexität für Variationsprobleme auf dem n-dimensionalen Torus. Manuscripta Math. 71 (1991) 45–65. [CrossRef] [MathSciNet]
  21. W. Senn, Differentiability properties of the minimal average action. Calc. Var. Partial Differential Equations 3 (1995) 343–384. [CrossRef] [MathSciNet]
  22. W. Senn, Equilibrium form of crystals and the stable norm. Z. angew. Math. Phys. 49 (1998) 919–933. [CrossRef] [MathSciNet]
  23. J.E. Taylor, Crystalline variational problems. BAMS 84 (1978) 568–588. [CrossRef] [MathSciNet]
  24. M.E. Taylor, Partial Differential Equations, Basic Theory Springer, Berlin (1996).
  25. N. Wiener, The ergodic theorem. Duke Math. J 5 (1939) 1–18. [CrossRef] [MathSciNet]