On the energy of type-II superconductors in the mixed phase

Reviews in Mathematical Physics

Volumn 12, Issue 9, 2000, Pages 1219-1257

  Sandier, Etienne ^a   Serfaty, Sylvia ^b,c  

^a UNIVERSITÉ DE TOURS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034356866     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X00000411     Document Type: Article

References (27)

1. A. Abrikosov, "On the magnetic properties of superconductors of the second type", Soviet Phys. JETP 5 (1957) 1174-1182.
2. L. Almeida and F. Bethuel, "Topological methods for the Ginzburg-Landau equations", J. Math. Pures Appl. 77 (1998) 1-49.
3. F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, 1994.
4. P. Bauman, N. Carlson and D. Phillips, "On the zeros of solutions to Ginzburg-Landau type systems", SIAM J. Math. Anal. 24(5) (1993) 1283-1293.
5. J Bardeen, L. N. Cooper and J. R. Schrieffer, "Theory of superconductivity", Phys. Rev., II. Ser. 108 (1957) 1175-1204.
6. F. Bethuel and T. Rivière, "Vortices for a variational problem related to superconductivity", Annales IHP, Analyse non linéaire 12 (1995) 243-303.
7. F. Bethuel and T. Rivière, "Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité", Séminaire E.D.P de l'École Polytechnique, exposé XVI, 1994.
8. M. Comte and P. Mironescu, "Etude d'un minimiseur de l'énergie de Ginzburg-Landau près de ses zéros", C. R. Acad. Sci., Paris, Ser. I 320(3) (1995) 289-293.
9. M. Comte and P. Mironescu, "The behavior of a Ginzburg-Landau minimizer near its zeroes", Calc. Var. Partial Differ. Equ. 4(4) (1996) 323-340.
10. P. G. DeGennes, Superconductivity of Metal and Alloys, Benjamin, New York and Amsterdam, 1966.
11. V. L. Ginzburg and L. D. Landau, in Collected Papers of L. D. Landau, ed. D. Ter Haar, Pergamon Press, Oxford, 1965.
12. T. Giorgi and D. Phillips, "The breakdown of superconductivity due to strong fields for the Ginzburg-Landau Model". SIAM Jour. Math. Anal. 30(2) (1999) 341-359.
13. R. Jerrard, "Lower bounds for generalized Ginzburg-Landau functionals", SIAM J. Math. Anal. 30 No. 4 (1999), 721-746.
14. P. Mironescu, "Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale", C. R. Acad. Sci., Paris, Ser. I 323(6) (1996) 593-598.
15. F. Pacard and T. Rivière, "Linear and Nonlinear aspects of vortices. The Ginzburg-Landau Model", Progress in nonlinear PDEs and their applications 39, Birkhäuser, 342p, (2000).
16. J. Rubinstein, "Six lectures on superconductivity", Proc. of the CRM School on Boundaries, interfaces, and transitions.
17. E. Sandier, "Lower bounds for the energy of unit vector fields and applications", J. Functional Analysis 152(2) (1998) 379-403;
18. Erratum, Ibid., 171(1) (2000).
19. S. Serfaty, "Solutions stables de l'équation de Ginzburg-Landau en présence de champ magnétique", C. R. Acad. Sci., Paris, Série I. 326(8), (1998) 949-954.
20. S. Serfaty, "Local minimizers for the Ginzburg-Landau energy near critical magnetic field", part I, Comm. Contemporary Math., Vol. 1, No. 2 (1999), 213-254.
21. S. Serfaty, "Local minimizers for the Ginzburg-Landau energy near critical magnetic field", part II, Comm. Contemporary Math., Vol. 1, No. 3 (1999), 295-333.
22. S. Serfaty, "Stable configurations in superconductivity: Uniqueness, multiplicity and vortex-nucleation", Arch. for Rat. Mech. Anal, 149(4) (1999), 329-365.
23. S. Serfaty, "Sur l'équation de Ginzburg-Landau avec champ magnétique", Proc. "Journées Équations aux dérivées partielles, Saint-Jean-de-Monts", 1998.
24. E. Sandier and S. Serfaty, "Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field", to appear in Annales IHP, Analyse non linéaire.
25. D. Saint-James, G. Sarma and E. J. Thomas, Type-II Superconductivity, Pergamon Press, 1969.
26. M. Tinkham, Introduction to Superconductivity, 2nd edition, McGraw-Hill, 1996.
27. D. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd edition, Adam Hilger Ltd., Bristol, 1986.