A rigorous derivation of free-boundary problem arising in superconductivity
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 4, pp. 561-592. 
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     author = {Sandier, Etienne and Serfaty, Sylvia},
     title = {A rigorous derivation of free-boundary problem arising in superconductivity},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {561--592},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {4},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00122-1},
     mrnumber = {2002k:35324},
     zbl = {01702168},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)00122-1/}
}
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Sandier, Etienne; Serfaty, Sylvia. A rigorous derivation of free-boundary problem arising in superconductivity. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 4, pp. 561-592. doi : 10.1016/s0012-9593(00)00122-1. http://www.numdam.org/articles/10.1016/s0012-9593(00)00122-1/

[1] Almeida L., Bethuel F., Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl. 77 (1998) 1-49. | MR | Zbl

[2] Aftalion A., Sandier E., Serfaty S., Pinning phenomena in the Ginzburg-Landau model of superconductivity, Preprint.

[3] Berestycki H., Bonnet A., Chapman J., A semi-elliptic system arising in the theory of type-II superconductivity, Comm. Appl. Nonlinear Anal. 1 (3) (1994) 1-21. | MR | Zbl

[4] Bethuel F., Brezis H., Hélein F., Ginzburg-Landau Vortices, Birkhäuser, 1994. | MR | Zbl

[5] Bonnet A., Monneau R., Existence of a smooth free-boundary in a superconductor with a Nash-Moser inverse function theorem argument, Interfaces and Free Boundaries (to appear).

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

[7] Cioranescu D., Murat F., Un terme étrange venu d'ailleurs, in : Nonlinear Partial Differential Equations and their Applications, Coll. de France Semin. Vol. II, Res. Notes Math., Vol. 60, 1982, pp. 98-138. | MR | Zbl

[8] Chapman S.J., Rubinstein J., Schatzman M., A mean-field model of superconducting vortices, Eur. J. Appl. Math. 7 (2) (1996) 97-111. | MR | Zbl

[9] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal. 30 (2) (1999) 341-359 (electronic). | MR | Zbl

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

[11] Murat F., L'injection du cône positif de H-1 dans W-1,q est compacte pour tout q < 2, J. Math. Pures Appl. 60 (1981) 309-322. | MR | Zbl

[12] Rodrigues J.F., Obstacle Problems in Mathematical Physics, Mathematical Studies, North-Holland, 1987. | MR | Zbl

[13] Sandier E., Lower bounds for the energy of unit vector fields and application, J. Functional Anal. 152 (2) (1998) 379-403. | MR | Zbl

[14] Sandier E., Serfaty S., Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field, Annales IHP, Analyse non Linéaire 17 (1) (2000) 119-145. | Numdam | MR | Zbl

[15] Sandier E., Serfaty S., On the energy of type-II superconductors in the mixed phase, Reviews in Math. Phys. (to appear). | Zbl

[16] Serfaty S., Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part I, Comm. Contemp. Math. 1 (2) (1999) 213-254. | MR | Zbl

[17] Serfaty S., Local minimizers for the Ginzburg-Landau energy near critical magnetic field, Part II, Comm. Contemp. Math. 1 (3) (1999) 295-333. | MR | Zbl

[18] Serfaty S., Stable configurations in superconductivity : Uniqueness, multiplicity and vortex-nucleation, Arch. Rat. Mech. Anal. 149 (1999) 329-365. | MR | Zbl

[19] Tinkham M., Introduction to Superconductivity, 2nd edn., McGraw-Hill, 1996.

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