Liquid crystals : relaxed energies, dipoles, singular lines and singular points

M. Giaquinta; G. Modica; J. Souček

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 3, page 415-437
  • ISSN: 0391-173X

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Giaquinta, M., Modica, G., and Souček, J.. "Liquid crystals : relaxed energies, dipoles, singular lines and singular points." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.3 (1990): 415-437. <http://eudml.org/doc/84081>.

@article{Giaquinta1990,
author = {Giaquinta, M., Modica, G., Souček, J.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {geometric measure theory; integral representation; relaxation problem; energy functional of liquid crystals; representation result; Dirichlet problem; dipole; minimizer currents; line singularities; Cartesian currents with fractures},
language = {eng},
number = {3},
pages = {415-437},
publisher = {Scuola normale superiore},
title = {Liquid crystals : relaxed energies, dipoles, singular lines and singular points},
url = {http://eudml.org/doc/84081},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Giaquinta, M.
AU - Modica, G.
AU - Souček, J.
TI - Liquid crystals : relaxed energies, dipoles, singular lines and singular points
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 3
SP - 415
EP - 437
LA - eng
KW - geometric measure theory; integral representation; relaxation problem; energy functional of liquid crystals; representation result; Dirichlet problem; dipole; minimizer currents; line singularities; Cartesian currents with fractures
UR - http://eudml.org/doc/84081
ER -

References

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  1. [1] F. Almgrem - W. Browder - E.H. Lieb, Co-area, liquid crystals, and minimal surfaces, In DDT - a selection of Papers, Springer-Verlag, 1987. Zbl0645.58015
  2. [2] F. Bethuel, A characterization of maps in H1(B3,S2) which can be approximated by smooth maps, preprint. Zbl0708.58004
  3. [3] F. Bethuel - S. Brezis - J.M. Coron, Relaxed energies for harmonic maps, preprint. 
  4. [4] S. Brezis, Sk-valued maps with singularities, In "Topics in Calculus of Variations" Ed. M. Giaquinta, Lecture Notes in Math. n. 1365, Springer-Verlag1989. Zbl0684.49015
  5. [5] S. Brezis - J.M. Coron - E.H. Lieb, Harmonic maps with defects, Comm. Math. Phys.107 (1986), p. 649-705. Zbl0608.58016
  6. [6] J. Ericksen - D. Kinderlehrer, Theory and applications of liquid crystals, IMA Series vol. 5, Springer-Verlag1987. Zbl0713.76006
  7. [7] H. Federer, Geometric measure theory. Springer-Verlag, New York, 1969. Zbl0176.00801
  8. [8] M. Giaquinta - G. Modica - J. Sou, Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity, Archive for Rat. Mech. Anal.106 (1989) 97-159. Erratum and addendum, Archive for Rat. Mech. Anal.109 (1990), 385-392. Zbl0677.73014
  9. [9] M. Giaquinta - G. Modica - J. Sou, Cartesian currents and variational problems for mappings into spheres, Ann. Scuola Norm. Sup. Pisa16 (1989), 393-485. Zbl0713.49014
  10. [10] M. Giaquinta - G. Modica, J. Sou, The Dirichlet Energy of Mappings with values into the sphere, Manuscripta Math.65 (1989) 489-507. Zbl0678.49006
  11. [11] R. Hardt, Point and line singularities in liquid crystals, preprint. Zbl0752.49018
  12. [12] R. Hardt - D. Kinderlehrer - F.H. Lin, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys.105 (1986), 547-570. Zbl0611.35077
  13. [13] R. Hardt - F.H. Lin, A remark on H1 mappings, Manuscripta Math.56 (1986) 1010. Zbl0618.58015
  14. [14] Yu. G. Reshetnyak, Space Mappings with Bounded Distorsion, Translation of Mathematics Monographs n. 73, A.M.S., Providence. Zbl0667.30018

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