Vortex pinning with bounded fields for the Ginzburg-Landau equation
Andre, Nelly ; Bauman, Patricia ; Phillips, Dan
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 705-729 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2003__20_4_705_0,
     author = {Andre, Nelly and Bauman, Patricia and Phillips, Dan},
     title = {Vortex pinning with bounded fields for the Ginzburg-Landau equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {705-729},
     doi = {10.1016/S0294-1449(02)00021-5},
     zbl = {1040.35108},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_4_705_0}
}

Andre, Nelly; Bauman, Patricia; Phillips, Dan. Vortex pinning with bounded fields for the Ginzburg-Landau equation. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 705-729. doi : 10.1016/S0294-1449(02)00021-5. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_4_705_0/

[1] A. Aftalion, E. Sandier, S. Serfaty, Pinning phenomena in the Ginzburg-Landau model of superconductivity, Preprint. | MR 1826348

[2] Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math. 167 (3-4) (1991) 153-206. | MR 1120602 | Zbl 0756.46017

[3] Chapman S.J., Du Q., Gunzburger M.D., A Ginzburg-Landau type model of superconducting/normal junctions including Josephson junctions, Europ. J. Appl. Math. 6 (1995) 97-114. | MR 1331493 | Zbl 0843.35120

[4] Chapman S.J., Richardson G., Vortex pinning by inhomogeneities in type II superconductors, Phys. D 108 (4) (1997) 397-407. | MR 1474691 | Zbl 1039.82510

[5] 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. | MR 1664763 | Zbl 0920.35058

[6] Jaffe A., Taubes C., Vortices Monopoles, Birkhäuser, 1980. | MR 614447 | Zbl 0457.53034

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

[8] Jimbo S., Morita Y., Ginzburg-Landau equations and stable solutions in a rotational domain, SIAM J. Math. Anal. 27 (5) (1996) 1360-1385. | MR 1402445 | Zbl 0865.35016

[9] Jimbo S., Zhai J., Ginzburg-Landau equation with magnetic effect: non-simply-connected domains, J. Math. Soc. Japan 50 (3) (1998) 663-684. | MR 1626354 | Zbl 0912.58011

[10] Likharev K., Superconducting weak links, Rev. Mod. Phys. 51 (1979) 101-159.

[11] E. Sandier, S. Serfaty, Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field, Annals IHP, Analyse non linéaire, to appear. | Numdam | MR 1743433 | Zbl 0947.49004

[12] E. Sandier, S. Serfaty, On the energy of type II superconductors in the mixed phase, Rev. Math. Phys., to appear. | MR 1794239 | Zbl 0964.49006

[13] Rubinstein J., Sternberg P., Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents, Comm. Math. Phys. 179 (1) (1996) 257-263. | MR 1395224 | Zbl 0860.35131

[14] Schoen R., Uhlenbeck K., Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (2) (1983) 253-268. | MR 710054 | Zbl 0547.58020