A rigorous derivation of free-boundary problem arising in superconductivity
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 4, p. 561-592
@article{ASENS_2000_4_33_4_561_0,
     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},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {4},
     year = {2000},
     pages = {561-592},
     doi = {10.1016/s0012-9593(00)00122-1},
     zbl = {01702168},
     mrnumber = {2002k:35324},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2000_4_33_4_561_0}
}
Sandier, Etienne; Serfaty, Sylvia. A rigorous derivation of free-boundary problem arising in superconductivity. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 4, pp. 561-592. doi : 10.1016/s0012-9593(00)00122-1. http://www.numdam.org/item/ASENS_2000_4_33_4_561_0/

[1] Almeida L., Bethuel F., Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl. 77 (1998) 1-49. | MR 99f:35183 | Zbl 0904.35023

[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 95e:35192 | Zbl 0866.35030

[4] Bethuel F., Brezis H., Hélein F., Ginzburg-Landau Vortices, Birkhäuser, 1994. | MR 95c:58044 | Zbl 0802.35142

[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 96g:35045 | Zbl 0842.35119

[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 84e:35039a | Zbl 0496.35030

[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 97b:82111 | Zbl 0849.35135

[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 2000b:35235 | Zbl 0920.35058

[10] Jerrard R., Lower bounds for generalized Ginzburg-Landau functionals, SIAM J. Math. Anal. 30 (4) (1999) 721-746. | MR 2001f:35115 | Zbl 0928.35045

[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 83b:46045 | Zbl 0471.46020

[12] Rodrigues J.F., Obstacle Problems in Mathematical Physics, Mathematical Studies, North-Holland, 1987. | MR 88d:35006 | Zbl 0606.73017

[13] Sandier E., Lower bounds for the energy of unit vector fields and application, J. Functional Anal. 152 (2) (1998) 379-403. | MR 99b:58056 | Zbl 0908.58004

[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 2001i:58039 | Zbl 0947.49004

[15] Sandier E., Serfaty S., On the energy of type-II superconductors in the mixed phase, Reviews in Math. Phys. (to appear). | Zbl 0964.49006

[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 2001a:82077 | Zbl 0944.49007

[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 2001f:82089 | Zbl 0964.49005

[18] Serfaty S., Stable configurations in superconductivity : Uniqueness, multiplicity and vortex-nucleation, Arch. Rat. Mech. Anal. 149 (1999) 329-365. | MR 2001h:82114 | Zbl 0959.35154

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