On the Ginzburg–Landau model of a superconducting ball in a uniform field

 Access to full text

 Full (PDF)

1. [1] Aftalion A., Jerrard R., Properties of a single vortex solution in a rotation Bose–Einstein condensate, C. R. Acad. Sci. Paris, Ser. I336 (2003) 713-718. Zbl1050.82502MR1988308
2. [2] G. Alberti, S. Baldo, G. Orlandi, Variational convergence for functionals of the Ginzburg–Landau type, Preprint, 2003. Zbl1160.35013MR2177107
3. [3] Bethuel F., Brezis H., Hélein F., Ginzburg–Landau Vortices, Birkhäuser, Basel, 1994. Zbl0802.35142MR1269538
4. [4] Bethuel F., Brezis H., Orlandi G., Asymptotics for the Ginzburg–Landau equation in arbitrary dimensions, J. Func. Anal.186 (2001) 432-520. Zbl1077.35047MR1864830
5. [5] Bethuel F., Rivière T., Bethuel F., Rivière T., Vortices for a variational problem related to superconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire12 (1995) 243-303. Zbl0842.35119MR1340265
6. [6] D. Chiron, Boundary problems for the Ginzburg–Landau equation, Preprint, Commun. Cont. Math., in press. Zbl1124.35081MR2175092
7. [7] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
8. [8] D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Revised third printing, Springer-Verlag, 1998. Zbl1042.35002
9. [9] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields in the Ginzburg–Landau model, SIAM J. Math. Anal.30 (2) (1999) 341-359. Zbl0920.35058MR1664763
10. [10] Giusti E., Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984. Zbl0545.49018MR775682
11. [11] Iwaniec T., Scott C., Stroffolini B., Nonlinear Hodge theory on manifolds with boundary, Ann. Mat. Pura Appl. (4)CLXXVII (1999) 37-115. Zbl0963.58003MR1747627
12. [12] R.L. Jerrard, More about Bose Einstein condensates, Preprint, 2003. 
13. [13] Jerrard R., Montero A., Sternberg P., Local minimizers of the Ginzburg–Landau energy with magnetic field in three dimensions, Comm. Math. Phys.249 (3) (2004) 549-577. Zbl1065.58012MR2084007
14. [14] Jerrard R., Soner H.M., The Jacobian and the Ginzburg–Landau energy, Calc. Var. Partial Differential Equations14 (2) (2002) 151-191. Zbl1034.35025MR1890398
15. [15] Kohn R.V., Sternberg P., Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Ser. A111 (1989) 69-84. Zbl0676.49011MR985990
16. [16] Ladyzhenskaya O., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, 1969. Zbl0184.52603MR254401
17. [17] Lin F.H., Rivière T., Complex Ginzburg–Landau equations in higher dimensions and codimension two area minimizing currents, J. Eur. Math. Soc.1 (1999) 237-322. Zbl0939.35056MR1714735
18. [18] London F., Superfluids, Wiley, New York, 1950. Zbl0058.23405
19. [19] Montero A., Sternberg P., Ziemer W., Local minimizers with vortices to the Ginzburg–Landau system in three dimensions, CPAMLVII (2004) 0099-0125. Zbl1052.49002
20. [20] Rivière T., Line vortices in the $U\left(1\right)$-Higgs model, ESAIM Control Optim. Calc. Var.1 (1996) 77-167. Zbl0874.53019MR1394302
21. [21] Sandier E., Ginzburg–Landau minimizers from $R^{n+1}$ to $R^n$ and minimal connections, Indiana Univ. Math. J.50 (4) (2001) 1807-1844. Zbl1034.58016MR1889083
22. [22] Sandier E., Serfaty S., A product estimate for Ginzburg–Landau and corollaries, J. Funct. Anal.211 (1) (2004) 219-244. Zbl1063.35144MR2054623
23. [23] Sandier E., Serfaty S., Ginzburg–Landau minimizers near the first critical field have bounded vorticity, Calc. Var. Partial Differential Equations17 (1) (2003) 17-28. Zbl1037.49001MR1979114
24. [24] Serfaty S., Local minimizers for the Ginzburg–Landau energy near critical magnetic field I, Comm. Cont. Math.1 (3) (1999) 295-333. Zbl0964.49005MR1707887
25. [25] Tinkham M., Superconductivity, Gordon and Breach, 1965. 
26. [26] Weyl H., The method of orthogonal projection in potential theory, Duke Math. J.7 (1940) 411-444. Zbl66.0444.01MR3331JFM66.0444.01
27. [27] Ziemer W.P., Weakly Differentiable Functions, Springer-Verlag, 1989. Zbl0692.46022MR1014685