Vortex pinning with bounded fields for the Ginzburg–Landau equation
Nelly Andre; Patricia Bauman; Dan Phillips
Annales de l'I.H.P. Analyse non linéaire (2003)
- Volume: 20, Issue: 4, page 705-729
- ISSN: 0294-1449
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top- [1] A. Aftalion, E. Sandier, S. Serfaty, Pinning phenomena in the Ginzburg–Landau model of superconductivity, Preprint. Zbl1027.35123MR1826348
- [2] Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (3–4) (1991) 153-206. Zbl0756.46017MR1120602
- [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. Zbl0843.35120MR1331493
- [4] Chapman S.J., Richardson G., Vortex pinning by inhomogeneities in type II superconductors, Phys. D108 (4) (1997) 397-407. Zbl1039.82510MR1474691
- [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. Zbl0920.35058MR1664763
- [6] Jaffe A., Taubes C., Vortices Monopoles, Birkhäuser, 1980. Zbl0457.53034MR614447
- [7] Jerrard R., Lower bounds for generalized Ginzburg–Landau functionals, SIAM J. Math. Anal.30 (4) (1999) 721-746. Zbl0928.35045MR1684723
- [8] Jimbo S., Morita Y., Ginzburg–Landau equations and stable solutions in a rotational domain, SIAM J. Math. Anal.27 (5) (1996) 1360-1385. Zbl0865.35016MR1402445
- [9] Jimbo S., Zhai J., Ginzburg–Landau equation with magnetic effect: non-simply-connected domains, J. Math. Soc. Japan50 (3) (1998) 663-684. Zbl0912.58011MR1626354
- [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. Zbl0947.49004MR1743433
- [12] E. Sandier, S. Serfaty, On the energy of type II superconductors in the mixed phase, Rev. Math. Phys., to appear. Zbl0964.49006MR1794239
- [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. Zbl0860.35131MR1395224
- [14] Schoen R., Uhlenbeck K., Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom.18 (2) (1983) 253-268. Zbl0547.58020MR710054