Free Access
Volume 16, Number 3, July-September 2010
Page(s) 545 - 580
Published online 18 June 2009
  1. A. Aftalion, E. Sandier and S. Serfaty, Pinning phenomena in the Ginzburg-Landau model of superconductivity. J. Math. Pures Appl. 80 (2001) 339–372. [CrossRef] [MathSciNet]
  2. A. Aftalion, S. Alama and L. Bronsard, Giant vortex and the breakdown of strong pinning in a rotating Bose-Einstein condensate. Arch. Rational Mech. Anal. 178 (2005) 247–286. [CrossRef]
  3. S. Alama and L. Bronsard, Pinning effects and their breakdown for a Ginzburg-Landau model with normal inclusions. J. Math. Phys. 46 (2005) 095102. [CrossRef] [MathSciNet]
  4. S. Alama and L. Bronsard, Vortices and pinning effects for the Ginzburg-Landau model in multiply connected domains. Comm. Pure Appl. Math. LIX (2006) 0036–0070.
  5. N. André, P. Baumann and D. Phillips, Vortex pinning with bounded fields for the Ginzburg-Landau equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 705–729. [CrossRef] [MathSciNet]
  6. H. Aydi and A. Kachmar, Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II. Comm. Pure Appl. Anal. 8 (2009) 977–998. [CrossRef]
  7. F. Béthuel and T. Rivière, Vortices for a variational problem related to superconductivity. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 243–303.
  8. F. Béthuel, H. Brezis and F. Hélein, Ginzburg-Landau vortices. Birkhäuser, Boston-Basel-Berlin (1994).
  9. S.J. Chapman and G. Richardson, Vortex pinning by inhomogenities in type II superconductors. Phys. D 108 (1997) 397–407. [CrossRef] [MathSciNet]
  10. S.J. Chapman, Q. Du and M.D. Gunzburger, A Ginzburg Landau type model of superconducting/normal junctions including Josephson junctions. European J. Appl. Math. 6 (1996) 97–114.
  11. P.G. de Gennes, Superconductivity of metals and alloys. Benjamin (1966).
  12. Q. Du, M. Gunzburger and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Reviews 34 (1992) 529–560. [CrossRef] [MathSciNet]
  13. H.J. Fink and W.C.H. Joiner, Surface nucleation and boundary conditions in superconductors. Phys. Rev. Lett. 23 (1969) 120. [CrossRef]
  14. T. Giorgi, Superconductors surrounded by normal materials. Proc. Roy. Soc. Edinburgh Sec. A 135 (2005) 331–356. [CrossRef]
  15. T. Giorgi and D. Phillips, The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model. SIAM J. Math. Anal. 30 (1999) 341–359. [CrossRef] [MathSciNet]
  16. J.O. Indekeu, F. Clarysse and E. Montevecchi, Wetting phase transition and superconductivity: The role of suface enhancement of the order parameter in the GL theory. Procceding of the NATO ASI, Albena, Bulgaria (1998).
  17. A. Kachmar, On the ground state energy for a magnetic Schrödinger operator and the effect of the de Gennes boundary condition. J. Math. Phys. 47 (2006) 072106. [CrossRef] [MathSciNet]
  18. A. Kachmar, On the perfect superconducting state for a generalized Ginzburg-Landau equation. Asymptot. Anal. 54 (2007) 125–164. [MathSciNet]
  19. A. Kachmar, On the stability of normal states for a generalized Ginzburg-Landau model. Asymptot. Anal. 55 (2007) 145–201. [MathSciNet]
  20. A. Kachmar, Weyl asymptotics for magnetic Schrödinger opertors and de Gennes' boundary condition. Rev. Math. Phys. 20 (2008) 901–932. [CrossRef] [MathSciNet]
  21. A. Kachmar, Magnetic Ginzburg-Landau functional with discontinuous constraint. C. R. Math. Acad. Sci. Paris 346 (2008) 297–300. [CrossRef] [MathSciNet]
  22. A. Kachmar, Limiting jump conditions for Josephson junctions in Ginzburg-Landau theory. Differential Integral Equations 21 (2008) 95–130. [MathSciNet]
  23. L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math. 77 (1999) 1–26. [CrossRef] [MathSciNet]
  24. K. Lu and X.-B. Pan, Ginzburg-Landau equation with de Gennes boundary condition. J. Diff. Equ. 129 (1996) 136-165. [CrossRef]
  25. N.G. Meyers, An Lp estimate for the gradient of solutions of second order elliptic equations. Ann. Sc. Norm. Sup. Pisa 17 (1963) 189–206.
  26. E. Montevecchi and J.O. Indekeu, Effects of confinement and surface enhancement on superconductivity. Phys. Rev. B 62 (2000) 661–666. [CrossRef]
  27. J. Rubinstein, Six lectures in superconductivity, in Boundaries, Interfaces and Transitions (Banff, AB, 1995), CRM Proc., Lecture Notes 13, Amer. Math. Soc., Providence, RI (1998) 163–184.
  28. E. Sandier and S. Serfaty, Ginzburg-Landau minimizers near the first critical field have bounded vorticity. Calc. Var. Partial Differ. Equ. 17 (2003) 17–28. [CrossRef]
  29. E. Sandier and S. Serfaty, Vortices for the magnetic Ginzburg-Landau model, Progress in Nonlinear Differential Equations and their Applications 70. Birkhäuser Boston (2007).
  30. S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field. I. Commun. Contemp. Math. 1 (1999) 213–254. [CrossRef] [MathSciNet]
  31. S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field. II. Commun. Contemp. Math. 1 (1999) 295–333. [CrossRef] [MathSciNet]
  32. I.M. Sigal and F. Ting, Pinning of magnetic vortices by an external potential. St. Petresburg Math. J. 16 (2005) 211–236. [CrossRef]
  33. G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus. Séminaire de Mathématiques Supérieures No. 16 (Été, 1965), Les Presses de l'Université de Montréal, Montréal, Québec (1966) 326 p.

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