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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  8. F. Béthuel, H. Brezis and F. Hélein, Ginzburg-Landau vortices. Birkhäuser, Boston-Basel-Berlin (1994). [Google Scholar]
  9. S.J. Chapman and G. Richardson, Vortex pinning by inhomogenities in type II superconductors. Phys. D 108 (1997) 397–407. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  11. P.G. de Gennes, Superconductivity of metals and alloys. Benjamin (1966). [Google Scholar]
  12. Q. Du, M. Gunzburger and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Reviews 34 (1992) 529–560. [Google Scholar]
  13. H.J. Fink and W.C.H. Joiner, Surface nucleation and boundary conditions in superconductors. Phys. Rev. Lett. 23 (1969) 120. [CrossRef] [Google Scholar]
  14. T. Giorgi, Superconductors surrounded by normal materials. Proc. Roy. Soc. Edinburgh Sec. A 135 (2005) 331–356. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  18. A. Kachmar, On the perfect superconducting state for a generalized Ginzburg-Landau equation. Asymptot. Anal. 54 (2007) 125–164. [MathSciNet] [Google Scholar]
  19. A. Kachmar, On the stability of normal states for a generalized Ginzburg-Landau model. Asymptot. Anal. 55 (2007) 145–201. [MathSciNet] [Google Scholar]
  20. A. Kachmar, Weyl asymptotics for magnetic Schrödinger opertors and de Gennes' boundary condition. Rev. Math. Phys. 20 (2008) 901–932. [CrossRef] [MathSciNet] [Google Scholar]
  21. A. Kachmar, Magnetic Ginzburg-Landau functional with discontinuous constraint. C. R. Math. Acad. Sci. Paris 346 (2008) 297–300. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Kachmar, Limiting jump conditions for Josephson junctions in Ginzburg-Landau theory. Differential Integral Equations 21 (2008) 95–130. [MathSciNet] [Google Scholar]
  23. L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math. 77 (1999) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  24. K. Lu and X.-B. Pan, Ginzburg-Landau equation with de Gennes boundary condition. J. Diff. Equ. 129 (1996) 136-165. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  26. E. Montevecchi and J.O. Indekeu, Effects of confinement and surface enhancement on superconductivity. Phys. Rev. B 62 (2000) 661–666. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  30. S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field. I. Commun. Contemp. Math. 1 (1999) 213–254. [Google Scholar]
  31. S. Serfaty, Local minimizers for the Ginzburg-Landau energy near critical magnetic field. II. Commun. Contemp. Math. 1 (1999) 295–333. [Google Scholar]
  32. I.M. Sigal and F. Ting, Pinning of magnetic vortices by an external potential. St. Petresburg Math. J. 16 (2005) 211–236. [CrossRef] [Google Scholar]
  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. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.