Some constancy results for nematic liquid crystals and harmonic maps

Kai Seng Chou; Xi-Ping Zhu

Annales de l'I.H.P. Analyse non linéaire (1995)

  • Volume: 12, Issue: 1, page 99-115
  • ISSN: 0294-1449

How to cite

top

Chou, Kai Seng, and Zhu, Xi-Ping. "Some constancy results for nematic liquid crystals and harmonic maps." Annales de l'I.H.P. Analyse non linéaire 12.1 (1995): 99-115. <http://eudml.org/doc/78354>.

@article{Chou1995,
author = {Chou, Kai Seng, Zhu, Xi-Ping},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {harmonic maps; Pokhozaev identity},
language = {eng},
number = {1},
pages = {99-115},
publisher = {Gauthier-Villars},
title = {Some constancy results for nematic liquid crystals and harmonic maps},
url = {http://eudml.org/doc/78354},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Chou, Kai Seng
AU - Zhu, Xi-Ping
TI - Some constancy results for nematic liquid crystals and harmonic maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 1
SP - 99
EP - 115
LA - eng
KW - harmonic maps; Pokhozaev identity
UR - http://eudml.org/doc/78354
ER -

References

top
  1. [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. Zbl0678.35086MR1002036
  2. [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. Zbl0649.35033MR929280
  3. [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. Zbl0706.35027MR1058505
  4. [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. Zbl0793.58011MR1205144
  5. [4] W. Ding, Positive solutions of Δu+u(n+2)/(n-2) = 0 on a contractible domain, preprint. MR1027983
  6. [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. 
  7. [6] R. Hardt and D. Kinderlehrer, Mathematical questions of liquid crystal theory, in Theory and Applications of Liquid Crystals, IMA, 5, Springer-Verlag, 1986. Zbl0704.76005MR900833
  8. [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. Zbl0611.35077MR852090
  9. [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. Zbl0544.58008MR765831
  10. [9] L. Lemaire, Applications harmoniques de surfaces riemanniennes, J. Diff. Geom., Vol. 13, 1978, pp. 51-78. Zbl0388.58003MR520601
  11. [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. Zbl0703.35173MR1003435
  12. [11] S.I. Pohozaev, Eigenfunction of the equation Δu + λf (u) = 0, Soviet Math. Dokl., Vol. 6, 1965, pp. 1408-1411. 
  13. [12] P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J., Vol. 35, 1986, pp. 681-703. Zbl0625.35027MR855181

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.