Minimal solutions of variational problems on a torus
Moser, Jürgen
Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986), p. 229-272 / Harvested from Numdam
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@article{AIHPC_1986__3_3_229_0,
     author = {Moser, J\"urgen},
     title = {Minimal solutions of variational problems on a torus},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {3},
     year = {1986},
     pages = {229-272},
     mrnumber = {847308},
     zbl = {0609.49029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1986__3_3_229_0}
}

Moser, Jürgen. Minimal solutions of variational problems on a torus. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) pp. 229-272. http://gdmltest.u-ga.fr/item/AIHPC_1986__3_3_229_0/

[1] M. Amann, M.G. Crandall, On Some Existence Theorems for Semi-linear Elliptic Equations, Ind. Univ. Math. Journal, t. 27, 1978, p. 779-790 (see esp. prop. 2 and its proof, p. 788-789. | MR 503713 | Zbl 0391.35030

[2] S. Aubry, P.Y. Le Daeron, The discrete Frenkel-Kantorova model and its extensions I. Exact results for the ground states, Physica, t. 8D, 1983, p. 381-422. | MR 719634

[3] V. Bangert, Mather Sets for Twist Maps and Geodesic Tori. Preprint, Bonn, 1985. | MR 945963

[4] E. De Giorgi, Sulla differenziabilità e l'analiticità degli integrali multipli regolari, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Natur, (3), n° 3, 1957, p. 25-43. | MR 93649 | Zbl 0084.31901

[5] E. Di Benedetto, N.S. Trudinger, Harnack Inequality for Quasi-Minima of Variational Integrals, Annales de l'Inst. H. Poincaré, Analyse Non-linéaire, t. 1, 1984, p. 295-308. | Numdam | MR 778976 | Zbl 0565.35012

[6] G. Eisen, Ueber die Regularität schwacher Lösungen von Variationsproblemen mit Hindernissen und Integralbedingungen, preprint No. 512, Sonderforschungsbereich 72, Universität Bonn, 1982.

[7] M. Giaquinta, E. Giusti, Quasi-Minima, Ann. d'Inst. Henri Poincaré, Analyse non lin., t. 1, 1984, p. 79-107. | Numdam | MR 778969 | Zbl 0541.49008

[8] M. Giaquinta, E. Giusti, On the regularity of the minima of variational integrals, Acta math., t. 148, 1982, p. 31-46. | MR 666107 | Zbl 0494.49031

[9] M. Giaquinta, E. Giusti, Differentiability of Minima of Non-Differentiable Functionals, Inv. math., t. 72, 1983, p. 285-298. | MR 700772 | Zbl 0513.49003

[10] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. Math. Studies, t. 105, Princeton, N. J., 1983. | MR 717034 | Zbl 0516.49003

[11] M. Giaquinta, An Introduction to the Regularity Theory for Nonlinear Elliptic Systems, Lecture Notes at the ETH Zürich, May 1984.

[12] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, 1983. | MR 737190 | Zbl 0562.35001

[13] G.A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. Math., t. 33, 1932, p. 719-739. | MR 1503086 | Zbl 0006.32601

[14] A. Katok, Some remarks on Birkhoff and Mather twist theorems, Ergodic Theory and Dynamical Systems, t. 2, 1982, p. 185-194. | MR 693974 | Zbl 0521.58048

[15] O.A. Ladyzhenskaya, N.N. Uraltseva, Linear and Quasilinear Elliptic Equations, Acad. Press, New York and London, 1968. | MR 244627 | Zbl 0164.13002

[16] J.N. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, t. 21, 1982, p. 457-467. | MR 670747 | Zbl 0506.58032

[17] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966. | MR 202511 | Zbl 0142.38701

[18] M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one. Trans. Am. Math. Soc., t. 26, 1924, p. 25-60. | JFM 50.0466.04 | MR 1501263

[19] J. Moser, On Harnack's Theorem for Elliptic Differential Equations, Comm. Pure Appl. Math., t. 14, 1961, p. 577-591. | MR 159138 | Zbl 0111.09302

[20] J. Moser, Monotone Twist Mappings and the Calculus of Variations, to appear in Dynamical Systems and Ergodic Theory, 1986. | MR 863203 | Zbl 0619.49020

[21] J. Moser, Breakdown of stability, to appear in SIAM Review, 1986.

[22] I.C. Percival, Variational principles for invariant tori and Cantori, A. I. P. Conference Proceedings No. 57, ed. M. Month, 1980, p. 1-17. | MR 624989

[23] I.C. Percival, A variational principle for invariant tori of fixed frequency, Journ. Phys. A., Math. Gen., t. 12, 1979, L 57-60. | MR 524167 | Zbl 0394.70018

[24] M. Protter, H. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, 1967. | MR 219861 | Zbl 0153.13602

[25] B. Solomon, On foliations of Rn+1 by minimal hypersurfaces, preprint from Indiana University, Oct. 1984, to appear in Comm. Math. Helv., 1986. | MR 847521 | Zbl 0601.53025

[26] N.S. Trudinger, On Harnack Type Inequalities and their Application to Quasilinear Elliptic Equations. Comm. Pure Appl. Math., t. 20, 1967, p. 721-747. | MR 226198 | Zbl 0153.42703