no. 2
From constant to non-degenerately vanishing magnetic fields in superconductivity
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 423-438.

We explore the relationship between two reference functions arising in the analysis of the Ginzburg–Landau functional. The first function describes the distribution of superconductivity in a type II superconductor subjected to a constant magnetic field. The second function describes the distribution of superconductivity in a type II superconductor submitted to a variable magnetic field that vanishes non-degenerately along a smooth curve.

DOI : 10.1016/j.anihpc.2015.12.008
Mots clés : Ginzburg–Landau functional, Non-degenerately vanishing magnetic fields, Energy asymptotics 
@article{AIHPC_2017__34_2_423_0,
     author = {Helffer, Bernard and Kachmar, Ayman},
     title = {From constant to non-degenerately vanishing magnetic fields in superconductivity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {423--438},
     publisher = {Elsevier},
     volume = {34},
     number = {2},
     year = {2017},
     doi = {10.1016/j.anihpc.2015.12.008},
     mrnumber = {3610939},
     zbl = {1361.82039},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2015.12.008/}
}
TY  - JOUR
AU  - Helffer, Bernard
AU  - Kachmar, Ayman
TI  - From constant to non-degenerately vanishing magnetic fields in superconductivity
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2017
SP  - 423
EP  - 438
VL  - 34
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2015.12.008/
DO  - 10.1016/j.anihpc.2015.12.008
LA  - en
ID  - AIHPC_2017__34_2_423_0
ER  - 
%0 Journal Article
%A Helffer, Bernard
%A Kachmar, Ayman
%T From constant to non-degenerately vanishing magnetic fields in superconductivity
%J Annales de l'I.H.P. Analyse non linéaire
%D 2017
%P 423-438
%V 34
%N 2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2015.12.008/
%R 10.1016/j.anihpc.2015.12.008
%G en
%F AIHPC_2017__34_2_423_0
Helffer, Bernard; Kachmar, Ayman. From constant to non-degenerately vanishing magnetic fields in superconductivity. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 423-438. doi : 10.1016/j.anihpc.2015.12.008. http://archive.numdam.org/articles/10.1016/j.anihpc.2015.12.008/

[1] Attar, K. The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field, Ann. Inst. Henri Poincaré, Anal. Non Linéaire., Volume 32 (2015), pp. 325–345 | DOI | Numdam | MR | Zbl

[2] Attar, K. Energy and vorticity of the Ginzburg–Landau model with variable magnetic field, Asymptot. Anal., Volume 93 (2015), pp. 75–114 | MR | Zbl

[3] Attar, K. Pinning with a variable magnetic field of the two dimensional Ginzburg–Landau model, 2015 (preprint) | arXiv

[4] Bonnaillie, V. On the fundamental state for a Schrödinger operator with magnetic fields in domains with corners, Asymptot. Anal., Volume 41 (2015) no. 3–4, pp. 215–258 | MR | Zbl

[5] Contreras, A.; Lamy, X. Persistence of superconductivity in thin shells beyond Hc1 , 2014 (Commun. Contemp. Math.) | arXiv | DOI | MR

[6] Fournais, S.; Helffer, B. Spectral Methods in Surface Superconductivity, Prog. Nonlinear Differ. Equ. Appl., vol. 77, Birkhäuser, 2010 | MR | Zbl

[7] Fournais, S.; Kachmar, A. The ground state energy of the three dimensional Ginzburg–Landau functional. Part I. Bulk regime, Commun. Partial Differ. Equ., Volume 38 (2013), pp. 339–383 | DOI | MR | Zbl

[8] de Gennes, P.G. Boundary effects in superconductors, Rev. Mod. Phys. (January 1964) | DOI

[9] Helffer, B.; Kachmar, A. The Ginzburg–Landau functional with a vanishing magnetic field, Arch. Ration. Mech. Anal., Volume 218 (2015), pp. 55–122 | DOI | MR | Zbl

[10] Montgomery, R. Hearing the zero locus of a magnetic field, Commun. Math. Phys., Volume 168 (1995) no. 3, pp. 651–675 | DOI | MR | Zbl

[11] J.-P. Miqueu, Equation de Schrödinger avec un champ magnétique qui s'annule, Thèse de doctorat, in preparation.

[12] Pan, X.B. Upper critical field for superconductors with edges and corners, Calc. Var. Partial Differ. Equ., Volume 14 (2002) no. 4, pp. 447–482 | MR | Zbl

[13] Pan, X.B.; Kwek, K.H. Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains, Trans. Am. Math. Soc., Volume 354 (2002) no. 10, pp. 4201–4227 | MR | Zbl

[14] Sandier, E.; Serfaty, S. Vortices for the Magnetic Ginzburg–Landau Model, Progress in Nonlinear Differential Equations and their Applications, vol. 70, Birkhäuser, 2007 | DOI | MR | Zbl

[15] Sandier, E.; Serfaty, S. The decrease of bulk superconductivity close to the second critical field in the Ginzburg–Landau model, SIAM J. Math. Anal., Volume 34 (2003) no. 4, pp. 939–956 | DOI | MR | Zbl

Cité par Sources :