Some constancy results for nematic liquid crystals and harmonic maps
Chou, Kai Seng ; Zhu, Xi-Ping
Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995), p. 99-115 / Harvested from Numdam
Publié le : 1995-01-01
@article{AIHPC_1995__12_1_99_0,
     author = {Chou,   Kai Seng and Zhu, Xi-Ping},
     title = {Some constancy results for nematic liquid crystals and harmonic maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {12},
     year = {1995},
     pages = {99-115},
     zbl = {0843.35027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1995__12_1_99_0}
}
Chou, Kai Seng; Zhu, Xi-Ping. Some constancy results for nematic liquid crystals and harmonic maps. Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) pp. 99-115. http://gdmltest.u-ga.fr/item/AIHPC_1995__12_1_99_0/

[21] Y. Yang, Existence, regularity, and asymptotic behavior of the solutions to the Ginzburg-Landau equations on R3, Commun. Math. Phys., Vol. 123, 1989, pp. 147-161. | MR 1002036 | Zbl 0678.35086

[1] A. Bahri and J.M. Coron, On a nonlinear elliptic problem involving the critical Sobolev exponent: The effect of the topology of the domain, Com. Pure Appl. Math., Vol. 41, 1988, pp. 253-294. | MR 929280 | Zbl 0649.35033

[2] F. Bethuel and H. Brezis, Regularity of minimizers of relaxed energies for harmonic maps, C. R. Acad. Sci. Paris, t. 310, Series I, 1990, pp. 827-829. | MR 1058505 | Zbl 0706.35027

[3] F. Bethuel, H. Brezis and J.M. Coron, Relaxed energies for harmonic maps, in Variational Problems, H. BERESTYCKI, J. M. CORON and I. EKELAND eds., Birkhäuser, 1990. | MR 1205144 | Zbl 0793.58011

[4] W. Ding, Positive solutions of Δu+u(n+2)/(n-2) = 0 on a contractible domain, preprint. | MR 1027983

[5] J.L. Ericksen, Equilibrium theory of liquid crystals, in Advances in Liquid Crystals, 2, pp. 233-299, G. H. BROWN ed., New York: Academic Press, 1976.

[6] R. Hardt and D. Kinderlehrer, Mathematical questions of liquid crystal theory, in Theory and Applications of Liquid Crystals, IMA, 5, Springer-Verlag, 1986. | MR 900833

[7] R. Hardt, D. Kinderlehrer and F.H. Lin, Existence and partial regularity of static liquid crystal configurations, Com. Math. Phy., Vol. 105, 1986, pp. 547-570. | MR 852090 | Zbl 0611.35077

[8] H. Karcher and J.C. Wood, Non-existence results and growth properties for harmonic maps and forms, J. Reine Angew. Math., Vol. 353, 1984, pp. 165-180. | MR 765831 | Zbl 0544.58008

[9] L. Lemaire, Applications harmoniques de surfaces riemanniennes, J. Diff. Geom., Vol. 13, 1978, pp. 51-78. | MR 520601 | Zbl 0388.58003

[10] F.H. Lin, Nonlinear theory of defects in nematic liquid crystal; phase transition and flow phenomena, Com. Pure. Appl. Math., Vol. 42, 1989, pp. 789-814. | MR 1003435 | Zbl 0703.35173

[11] S.I. Pohozaev, Eigenfunction of the equation Δu + λf (u) = 0, Soviet Math. Dokl., Vol. 6, 1965, pp. 1408-1411.

[12] P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J., Vol. 35, 1986, pp. 681-703. | MR 855181 | Zbl 0625.35027