Vortices for a variational problem related to superconductivity

Fabrice Bethuel; Tristan Rivière

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

  • Volume: 12, Issue: 3, page 243-303
  • ISSN: 0294-1449

How to cite

top

Bethuel, Fabrice, and Rivière, Tristan. "Vortices for a variational problem related to superconductivity." Annales de l'I.H.P. Analyse non linéaire 12.3 (1995): 243-303. <http://eudml.org/doc/78359>.

@article{Bethuel1995,
author = {Bethuel, Fabrice, Rivière, Tristan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau equation; minimizers of Ginzburg-Landau functionals; superconductivity; Higgs models; vortices},
language = {eng},
number = {3},
pages = {243-303},
publisher = {Gauthier-Villars},
title = {Vortices for a variational problem related to superconductivity},
url = {http://eudml.org/doc/78359},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Bethuel, Fabrice
AU - Rivière, Tristan
TI - Vortices for a variational problem related to superconductivity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 3
SP - 243
EP - 303
LA - eng
KW - Ginzburg-Landau equation; minimizers of Ginzburg-Landau functionals; superconductivity; Higgs models; vortices
UR - http://eudml.org/doc/78359
ER -

References

top
  1. [1] F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of Variations, Vol. I, 1993, pp. 123-148. Zbl0834.35014MR1261720
  2. [2] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, 1993. Zbl0802.35142MR1269538
  3. [3] F. Bethuel, H. Brezis and F. Hélein, Limite singulière pour la minimisation de fonctionnelles du type Ginzburg-Landau, C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 891-895. Zbl0773.49003MR1168319
  4. [4] F. Bethuel, H. Brezis and F. Hélein, Tourbillons de Ginzburg-Landau et énergies renormalisées, to appear inC. R. Acad. Sci. Paris, 1993. Zbl0783.35014MR1231415
  5. [5] H. Brezis, F. Merle and T. Rivière, Quantization effects for -Δu = u (1 - |u|2) in R2, to appear in , Arch. for ratio. Mech.1993. Zbl0809.35019MR1228965
  6. [6] H. Brezis, F. Merle and T. Rivière, Quantifications pour les solutions de -Δu = u(1 - |u|2) dans R2, to appear in C..R. .Acad. Sci. Paris, 1993. MR1228965
  7. [7] A. Boutet de Monvel-Berthier, V. Georgescu and R. Purice, Sur un problème aux limites de la théorie de Ginzburg-Landau, C. R. Acad. Sci. Paris, Vol. 307, 1988, pp. 55-58. Zbl0696.35058MR954091
  8. [8] A. Comtet and G.W. Gibbons, Bogomol'nyi bounds for cosmic strings, Nucl. Phys. B, Vol. 299, 1988, pp. 719-733. MR936758
  9. [9] Q. Du, M. Gunzburger and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Review, Vol. 34, 1992, pp. 45-81. Zbl0787.65091MR1156289
  10. [10] P. Grisvard, Elliptic Problems in non-smooth domains, Pitman, Marshfields, Mass, 1985. Zbl0695.35060
  11. [11] A. Jaffe and C. Taubes, Vortices and Monopoles, Birkhäuser, 1980. Zbl0457.53034MR614447
  12. [12] D. Saint-James, G. Sarma and E.J. Thomas, Type II Superconductivity, Pergamon Press, 1969. 
  13. [13] J. Spruck and Y. Yang, Cosmic string solutions of the Einstein Matter gauge equations, to appear1993. 
  14. [14] J. Spruck and Y. Yang, On multivortices in the electroweak theory II: existence of Bogomol'nyi solutions in R2, Comm. Math. Phys., Vol. 144, 1992, pp. 215-234. Zbl0748.53060MR1152370
  15. [15] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Presses Univ. deMontreal, 1966. Zbl0151.15501MR251373
  16. [16] Y. Yang, Boundary value problems of the Ginzburg-Landau equations, Proc. Roy. Soc. Edinburgh, Vol. 114 A, 1990, pp. 355-365. Zbl0708.35074MR1055553

Citations in EuDML Documents

top
  1. Hassen Aydi, Etienne Sandier, Vortex analysis of the periodic Ginzburg-Landau model
  2. Tristan Rivière, Line vortices in the U(1) Higgs model
  3. Sylvia Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique
  4. S. Alama, A. J. Berlinsky, L. Bronsard, Minimizers of the Lawrence–Doniach energy in the small-coupling limit : finite width samples in a parallel field
  5. Etienne Sandier, Sylvia Serfaty, A rigorous derivation of free-boundary problem arising in superconductivity
  6. Sylvia Serfaty, Systems with Coulomb interactions
  7. Etienne Sandier, Sylvia Serfaty, Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field
  8. Stan Alama, Lia Bronsard, J. Alberto Montero, On the Ginzburg–Landau model of a superconducting ball in a uniform field
  9. Tristan Rivière, Asymptotic analysis for the Ginzburg-Landau equations
  10. Ayman Kachmar, Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

NotesEmbed ?

top

You must be logged in to post comments.