Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field
Sandier, Etienne ; Serfaty, Sylvia
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000), p. 119-145 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2000__17_1_119_0,
     author = {Sandier, \'Etienne and Serfaty, Sylvia},
     title = {Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {17},
     year = {2000},
     pages = {119-145},
     mrnumber = {1743433},
     zbl = {0947.49004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_1_119_0}
}

Sandier, Etienne; Serfaty, Sylvia. Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 119-145. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_1_119_0/

[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. | MR 1617594 | Zbl 0904.35023

[3] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, 1994. | MR 1269538 | Zbl 0802.35142

[4] F. Bethuel and T. Rivière, Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité, Séminaire E. D. P de l'École Polytechnique XVI (1994). | Numdam | MR 1300912 | Zbl 0876.35112

[5] F. Bethuel and T. Rivière, Vortices for a variational problem related to superconductivity, Annales IHP, Analyse non Linéaire 12 (1995) 243-303. | Numdam | MR 1340265 | Zbl 0842.35119

[6] P.G. Degennes, Superconductivity of Metal and Alloys, Benjamin, New York and Amsterdam, 1966. | Zbl 0138.22801

[7] R. Jerrard, Lower bounds for generalized Ginzburg-Landau Functionals, SIAM J. Math. Anal. 30 (4) (1999) 721-746. | MR 1684723 | Zbl 0928.35045

[8] J. Rubinstein, Six lectures on superconductivity, in: Proc. CRM School on "Boundaries, Interfaces, and Transitions". | MR 1619115 | Zbl 0921.35161

[9] D. Saint-James, G. Sarma and E.J. Thomas, Type-II Superconductivity, Pergamon Press, 1969.

[10] E. Sandier, Lower bounds for the energy of unit vector fields and applications, J. Functional Analysis 152 (2) (1998) 379-403. | MR 1607928 | Zbl 0908.58004

[11] E. Sandier and S. Serfaty, On the energy of type-II superconductors in the mixed phase, Preprint. | MR 1794239

[12] S. Serfaty, Solutions stables de l'équation de Ginzburg-Landau en présence de champ magnétique, C. R. A. S. I 326 (8) (1998) 955. | MR 1649937 | Zbl 0913.35134

[13] S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part I, Comm. Contemporary Mathematics, to appear. | Zbl 0944.49007

[14] S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part II, Comm. Contemporary Mathematics, to appear. | Zbl 0964.49005

[15] S. Serfaty, Stable configurations in superconductivity: Uniqueness, multiplicity and vortex-nucleation, Arch. for Rat. Mech. Anal., to appear. | MR 1731999 | Zbl 0959.35154

[16] S. Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique, in: Proc. "Journées Équations aux dérivées partielles, Saint-Jean-de-Monts", 1998. | Numdam | Zbl 01808721

[17] E.M. Stein, Harmonic Analysis, Princeton Math. Series, No 43, Princeton University Press, 1969.

[18] D. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd ed., Adam Hilger, Bristol, 1986.