Ginzburg-Landau vortices : the static model
Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 868, 31 p. 
@incollection{SB_1999-2000__42__73_0,
     author = {Rivi\`ere, Tristan},
     title = {Ginzburg-Landau vortices : the static model},
     booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
     series = {Ast\'erisque},
     note = {talk:868},
     pages = {73--103},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {276},
     year = {2002},
     mrnumber = {1886757},
     zbl = {1027.35131},
     language = {en},
     url = {http://archive.numdam.org/item/SB_1999-2000__42__73_0/}
}
TY  - CHAP
AU  - Rivière, Tristan
TI  - Ginzburg-Landau vortices : the static model
BT  - Séminaire Bourbaki : volume 1999/2000, exposés 865-879
AU  - Collectif
T3  - Astérisque
N1  - talk:868
PY  - 2002
SP  - 73
EP  - 103
IS  - 276
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_1999-2000__42__73_0/
LA  - en
ID  - SB_1999-2000__42__73_0
ER  - 
%0 Book Section
%A Rivière, Tristan
%T Ginzburg-Landau vortices : the static model
%B Séminaire Bourbaki : volume 1999/2000, exposés 865-879
%A Collectif
%S Astérisque
%Z talk:868
%D 2002
%P 73-103
%N 276
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_1999-2000__42__73_0/
%G en
%F SB_1999-2000__42__73_0
Rivière, Tristan. Ginzburg-Landau vortices : the static model, dans Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 868, 31 p. http://archive.numdam.org/item/SB_1999-2000__42__73_0/

[Ab] A. Abrikosov - On the magnetic properties of superconductors of the second type, Soviet Phys. JETP 5, 1174-1182 (1957).

[Af] A. Aftalion - On the minimizers of the Ginzburg-Landau energy for high kappa: the one-dimensional case, European J. Appl. Math. 8, 331-345 (1997). | MR | Zbl

[AT] A. Aftalion and C. Troy - On the solutions of the one dimensional Ginzburg-Landau Equations, Preprint LMENS (1998).

[AB1] L. Almeida and F. Bethuel - Multiplicity results for the Ginzburg-Landau equation in presence of symmetries, Houston J. Math. 23, 733-764 (1997). | MR | Zbl

[AB2] L. Almeida and F. Bethuel - Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl. 77, 1-49 (1998). | MR | Zbl

[BBC] H. Berestycki, A. Bonnet and J. Chapman - A semi-elliptic system arising in the theory of type-II superconductivity, Comm. Appl. Non-linear Anal. 1, 1-21 (1994). | Zbl

[BC] M. S. Berger and Y. Y. Chen - Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization, phenomenon, Journal of Funct. Anal. 82, 259-295 (1989). | MR | Zbl

[BBH0] F. Bethuel, H. Brezis, and F. Hélein - Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. Partial Differ. Equ. 1, 2, 123-148 (1993). | MR | Zbl

[BBH] F. Bethuel, H. Brezis and F. Hélein - Ginzburg-Landau vortices, Birkhäuser (1994). | MR | Zbl

[BR1] F. Bethuel and T. Rivière - Vortices for a variational problem related to supraconductivity, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, 3, 243-303 (1995). | Numdam | MR | Zbl

[BR2] F. Bethuel and T. Rivière - Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité, Seminaire EDP de l'École Polytechnique, exposé XVI (1994). | Numdam | MR | Zbl

[Bog] B. Bogomol'Nyi - Soviet J. Nucl. Phys. 24, 449 (1976). | MR

[BH1] C. Bolley and B. Helffer - Rigorous results on Ginzburg-Landau models in a film submitted to an exterior parallel magnetic field I and II, Non Linear Stud. 3, 1-29 and 121-152 (1996). | MR | Zbl

[BH2] C. Bolley and B. Helffer - The ginzburg-Landau equations in a semi-infinite superconducting film in the large κ limit, European J. Appl. Math. 8, 347-367 (1997). | Zbl

[BCM] A. Bonnet, J. Chapman and R. Monneau - Convergence of Meissner minimizers of the Ginzburg-Landau energy of superconductivity as κ → +∞, preprint (1999).

[BM] A. Bonnet and R. Monneau - Existence of a smooth free-boundary in a superconductor with a Nash-Moser inverse function theorem argument, preprint (1999).

[BBM] J. Bourgain, H. Brezis and P. Mironescu - Lifting properties of Sobolev maps, in preparation.

[BMR] H. Brezis, F. Merle and T. Rivière - Quantization effects for -Δu = u(1 - |u|2) in R2, Arch. Rat. Mech. Analysis. 126, 123-145 (1994). | Zbl

[DL] Q. Du and H. Lin - Ginzburg-Landau vortices: dynamics, pinning and hysteresis, Siam J. Math. Anal. 28, 1265-1293 (1997). | MR | Zbl

[D] M. Dutour - Bifurcation vers l'état d'Abrikosov et diagramme de phase, thèse de l'Université Paris-Sud, Orsay (1999).

[dG] G. De Gennes - Superconductivity of Metal and Alloys, Benjamin, New-York and Amsterdam (1966). | Zbl

[GS] S. Gueron and I. Shafrir - On a discrete variational problem involving interacting particles, to appear in SIAM J. Appl. Math. (1999). | MR | Zbl

[JT] A. Jaffe and C. Taubes - Vortices and Monopoles, Birkhäuser (1980). | MR | Zbl

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

[LL] H. Lin and C. Lin - Minimax solutions of the Ginzburg-Landau equations, Selecta Mathematica, New Series 3, 99-113 (1997). | MR | Zbl

[LR] H. Lin and T. Rivière - Complex Ginzburg-Landau equations and codimension 2 minimal surfaces, J.E.M.S. 1, 3 (1999).

[LR2] H. Lin and T. Rivière - A quantization property for static Ginzburg-Landau vortices, Comm. Pure and App. Math. (2000). | Zbl

[Mi] P. Mironescu - Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale, C.R. Acad. Sci. Paris, Ser. 1, 323, 593-598 (1996). | MR | Zbl

[OS] N. Ovchinnikov and M. Sigal - The Ginzburg-Landau equation I. Static vortices, Partial differential equations and their applications (Toronto, ON, 1995), 199-220, CRM Proc. Lecture Notes 12, Amer. Math. Soc., Providence, RI (1997). | MR | Zbl

[PR] F. Pacard and T. Rivière - Linear and non-linear aspects of vortices, Birkhäuser (2000). | MR | Zbl

[Qin] J. Qing - Renormalized energy for Ginzburg-Landau vortices on closed surfaces, Math. Z. 225, 1-34 (1997). | MR | Zbl

[Ri1] T. Rivière - Asymptotic analysis for the Ginzburg-Landau equations, ETH-Zürich course, January 1997, Boll U.M.I. (1999). | MR

[Ri2] T. Rivière - Line vortices in the U(1)-Higgs Model, COCV 1, 77-167 (1995). | Numdam | MR | Zbl

[Ri3] T. Rivière - Some progress towards Jaffe and Taubes Conjectures, preprint (1999).

[R] F. Rodrigues - Obstacle problems in mathematical physics, Mathematical Studies, North Holland (1987). | MR | Zbl

[SST] D. Saint-James, G. Sarma and J. Thomas - Type-II Superconductivity, Pergamon Press (1969).

[Sa] E. Sandier - Lower bounds for the energy of unit vector fields and applications, J. Funct. Anal. 152, 379-403 (1998). | MR | Zbl

[SS1] E. Sandier and S. Serfaty - Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field, to appear in Annales de l'Inst. Henri Poincaré, Analyse non-linéaire (1999). | Numdam | MR | Zbl

[SS2] E. Sandier and S. Serfaty - A rigourous derivation of a free-boundary problem arising in superconductivity, Ann. Sci. Éc. Norm. Sup. 33 (2000), 561-592. | Numdam | MR | Zbl

[Se1] S. Serfaty - Étude mathématique de l'équation de Ginzburg-Landau de la supraconductivité, Thèse de l'Université Paris-Sud, Orsay (1999).

[Se2] S. Serfaty - Local minimizers for the Ginzburg-Landau energy near critical magnetic field I and II, Comm. Contemporary Mathematics 1, n° 2 et 3, 213-254 (1999). | MR | Zbl

[Se3] S. Serfaty - Stable configurations in superconductivity: uniqueness, multiplicity and vortex-nucleation, to appear in : Arch. Rat. Mech. Anal. (1999). | MR | Zbl

[St] M. Struwe - On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, J. Diff. Int. Equations 7 (1994), 1613-1624 and Erratum in J. Diff. Int. | MR | Zbl

[Ti] M. Tinkham - Introduction to Superconductivity, 2nd edition, McGraw-Hill (1996).

[Uh] K. Uhlenbeck - Connections with Lp bounds on curvature, Comm. Math. Phys. 83, 31-42 (1982). | MR | Zbl