Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field

Etienne Sandier; Sylvia Serfaty

Annales de l'I.H.P. Analyse non linéaire (2000)

  • Volume: 17, Issue: 1, page 119-145
  • ISSN: 0294-1449

How to cite

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Sandier, Etienne, and Serfaty, Sylvia. "Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field." Annales de l'I.H.P. Analyse non linéaire 17.1 (2000): 119-145. <http://eudml.org/doc/78484>.

@article{Sandier2000,
author = {Sandier, Etienne, Serfaty, Sylvia},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {minimization problem; Ginzburg-Landau functional; vortex structure; Meissner solution},
language = {eng},
number = {1},
pages = {119-145},
publisher = {Gauthier-Villars},
title = {Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field},
url = {http://eudml.org/doc/78484},
volume = {17},
year = {2000},
}

TY - JOUR
AU - Sandier, Etienne
AU - Serfaty, Sylvia
TI - Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2000
PB - Gauthier-Villars
VL - 17
IS - 1
SP - 119
EP - 145
LA - eng
KW - minimization problem; Ginzburg-Landau functional; vortex structure; Meissner solution
UR - http://eudml.org/doc/78484
ER -

References

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  1. [1] A. Abrikosov, On the magnetic properties of superconductors of the second type, Soviet Phys. JETP5 (1957) 1174-1182. 
  2. [2] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl.77 (1998) 1-49. Zbl0904.35023MR1617594
  3. [3] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, 1994. Zbl0802.35142MR1269538
  4. [4] F. Bethuel and T. Rivière, Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité, Séminaire E. D. P de l'École PolytechniqueXVI (1994). Zbl0876.35112MR1300912
  5. [5] F. Bethuel and T. Rivière, Vortices for a variational problem related to superconductivity, Annales IHP, Analyse non Linéaire12 (1995) 243-303. Zbl0842.35119MR1340265
  6. [6] P.G. Degennes, Superconductivity of Metal and Alloys, Benjamin, New York and Amsterdam, 1966. Zbl0138.22801
  7. [7] R. Jerrard, Lower bounds for generalized Ginzburg-Landau Functionals, SIAM J. Math. Anal.30 (4) (1999) 721-746. Zbl0928.35045MR1684723
  8. [8] J. Rubinstein, Six lectures on superconductivity, in: Proc. CRM School on "Boundaries, Interfaces, and Transitions". Zbl0921.35161
  9. [9] D. Saint-James, G. Sarma and E.J. Thomas, Type-II Superconductivity, Pergamon Press, 1969. 
  10. [10] E. Sandier, Lower bounds for the energy of unit vector fields and applications, J. Functional Analysis152 (2) (1998) 379-403. Zbl0908.58004MR1607928
  11. [11] E. Sandier and S. Serfaty, On the energy of type-II superconductors in the mixed phase, Preprint. Zbl0964.49006MR1794239
  12. [12] S. Serfaty, Solutions stables de l'équation de Ginzburg-Landau en présence de champ magnétique, C. R. A. S. I326 (8) (1998) 955. Zbl0913.35134MR1649937
  13. [13] S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part I, Comm. Contemporary Mathematics, to appear. Zbl0944.49007
  14. [14] S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part II, Comm. Contemporary Mathematics, to appear. Zbl0964.49005
  15. [15] S. Serfaty, Stable configurations in superconductivity: Uniqueness, multiplicity and vortex-nucleation, Arch. for Rat. Mech. Anal., to appear. Zbl0959.35154MR1731999
  16. [16] S. Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique, in: Proc. "Journées Équations aux dérivées partielles, Saint-Jean-de-Monts", 1998. Zbl1213.58014
  17. [17] E.M. Stein, Harmonic Analysis, Princeton Math. Series, No 43, Princeton University Press, 1969. 
  18. [18] D. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd ed., Adam Hilger, Bristol, 1986. 

Citations in EuDML Documents

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  1. Daniel Spirn, Xiaodong Yan, Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy
  2. Nelly Andre, Patricia Bauman, Dan Phillips, Vortex pinning with bounded fields for the Ginzburg–Landau equation
  3. Etienne Sandier, Sylvia Serfaty, A rigorous derivation of free-boundary problem arising in superconductivity
  4. Sylvia Serfaty, On a model of rotating superfluids
  5. Sylvia Serfaty, On a model of rotating superfluids
  6. Sylvia Serfaty, Vorticité dans les équations de Ginzburg-Landau de la supraconductivité
  7. Tristan Rivière, Ginzburg-Landau vortices : the static model
  8. Bernard Helffer, Bouteilles magnétiques et supraconductivité

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