Upper critical field and location of surface nucleation of superconductivity
Helffer, Bernard ; Pan, Xing-Bin
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 145-181 / Harvested from Numdam
@article{AIHPC_2003__20_1_145_0,
     author = {Helffer, Bernard and Pan, Xing-Bin},
     title = {Upper critical field and location of surface nucleation of superconductivity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {145-181},
     mrnumber = {1958165},
     zbl = {1060.35132},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_1_145_0}
}
Helffer, Bernard; Pan, Xing-Bin. Upper critical field and location of surface nucleation of superconductivity. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 145-181. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_1_145_0/

[1] Agmon S., Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operators, Princeton University Press, 1982. | MR 745286 | Zbl 0503.35001

[2] Bauman P., Phillips D., Tang Q., Stable nucleation for the Ginzburg-Landau system with an applied magnetic field, Arch. Rational Mech. Anal. 142 (1998) 1-43. | MR 1629119 | Zbl 0922.35157

[3] Bernoff A., Sternberg P., Onset of superconductivity in decreasing fields for general domains, J. Math. Phys. 38 (1998) 1272-1284. | MR 1608449 | Zbl 1056.82523

[4] Bolley C., Helffer B., An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material, Ann. Inst. Henri Poincaré, Physique Théorique 58 (1993) 189-233. | Numdam | MR 1217119 | Zbl 0779.35104

[5] Chapman S.J., Nucleation of superconductivity in decreasing fields, European J. Appl. Math. 5 (1994), part 1, 449-468; part 2, 469-494. | MR 1309734 | Zbl 0820.35124

[6] Chapman S.J., Howison S.D., Ockendon J.R., Macroscopic models for superconductivity, SIAM Rev. 34 (1992) 529-560. | MR 1193011 | Zbl 0769.73068

[7] Dauge M., Helffer B., Eigenvalues variation, I, Neumann problem for Sturm-Liouville operators, J. Differential Equations 104 (1993) 243-262. | MR 1231468 | Zbl 0784.34021

[8] De Gennes P.G., Superconductivity of Metals and Alloys, Benjamin, New York, 1966. | Zbl 0138.22801

[9] Del Pino M., Felmer P., Sternberg P., Boundary concentration for eigenvalue problems related to the onset of superconductivity, Comm. Math. Phys. 210 (2000) 413-446. | MR 1776839 | Zbl 0982.35077

[10] Du Q., Gunzburger M., Peterson J., Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Rev. 34 (1992) 45-81. | MR 1156289 | Zbl 0787.65091

[11] Ginzburg V., Landau L., On the theory of superconductivity, Soviet Phys. JETP 20 (1950) 1064-1082.

[12] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal. 30 (1999) 341-359. | MR 1664763 | Zbl 0920.35058

[13] Helffer B., Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, 1336, Springer-Verlag, 1988. | MR 960278 | Zbl 0647.35002

[14] Helffer B., Mohamed A., Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal. 138 (1996) 40-81. | MR 1391630 | Zbl 0851.58046

[15] Helffer B., Morame A., Magnetic bottles in connection with superconductivity, J. Funct. Anal. 185 (2001) 604-680. | MR 1856278 | Zbl 1078.81023

[16] Lu K., Pan X.-B., The first eigenvalue of Ginzburg-Landau operator, in: Bates , (Eds.), Differential Equations and Applications, International Press, 1997, pp. 215-226. | MR 1602638 | Zbl 0935.35108

[17] Lu K., Pan X.-B., Gauge invariant eigenvalue problems in R2 and in R2+, Trans. Amer. Math. Soc. 352 (2000) 1247-1276. | MR 1675206 | Zbl 1053.35124

[18] Lu K., Pan X.-B., Eigenvalue problems of Ginzburg-Landau operator in bounded domains, J. Math. Phys. 40 (1999) 2647-2670. | MR 1694223 | Zbl 0943.35058

[19] Lu K., Pan X.-B., Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Phys. D 127 (1999) 73-104. | MR 1678383 | Zbl 0934.35174

[20] Lu K., Pan X.-B., Surface nucleation of superconductivity in 3-dimension, J. Differential Equations 168 (2000) 386-452. | MR 1808455 | Zbl 0972.35152

[21] Lu K., Pan X.-B., Surface nucleation of superconductivity, Methods and Applications of Analysis 8 (2001) 279-300. | MR 1904530 | Zbl 1016.35066

[22] Saint-James D., De Gennes P., Onset of superconductivity in decreasing fields, Phys. Lett. 6 (5) (1963) 306-308.

[23] Saint-James D., Sarma G., Thomas E.J., Type II Superconductivity, Pergamon Press, Oxford, 1969.

[24] Tinkham M., Introduction to Superconductivity, McGraw-Hill, New York, 1975.