@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}, pages = {145--181}, publisher = {Elsevier}, volume = {20}, number = {1}, year = {2003}, mrnumber = {1958165}, zbl = {1060.35132}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2003__20_1_145_0/} }
TY - JOUR AU - Helffer, Bernard AU - Pan, Xing-Bin TI - Upper critical field and location of surface nucleation of superconductivity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 145 EP - 181 VL - 20 IS - 1 PB - Elsevier UR - http://www.numdam.org/item/AIHPC_2003__20_1_145_0/ LA - en ID - AIHPC_2003__20_1_145_0 ER -
%0 Journal Article %A Helffer, Bernard %A Pan, Xing-Bin %T Upper critical field and location of surface nucleation of superconductivity %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 145-181 %V 20 %N 1 %I Elsevier %U http://www.numdam.org/item/AIHPC_2003__20_1_145_0/ %G en %F 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) no. 1, pp. 145-181. http://www.numdam.org/item/AIHPC_2003__20_1_145_0/
[1] Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operators, Princeton University Press, 1982. | MR | Zbl
,[2] Stable nucleation for the Ginzburg-Landau system with an applied magnetic field, Arch. Rational Mech. Anal. 142 (1998) 1-43. | MR | Zbl
, , ,[3] Onset of superconductivity in decreasing fields for general domains, J. Math. Phys. 38 (1998) 1272-1284. | MR | Zbl
, ,[4] 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 | Zbl
, ,[5] Nucleation of superconductivity in decreasing fields, European J. Appl. Math. 5 (1994), part 1, 449-468; part 2, 469-494. | MR | Zbl
,[6] Macroscopic models for superconductivity, SIAM Rev. 34 (1992) 529-560. | MR | Zbl
, , ,[7] Eigenvalues variation, I, Neumann problem for Sturm-Liouville operators, J. Differential Equations 104 (1993) 243-262. | MR | Zbl
, ,[8] Superconductivity of Metals and Alloys, Benjamin, New York, 1966. | Zbl
,[9] Boundary concentration for eigenvalue problems related to the onset of superconductivity, Comm. Math. Phys. 210 (2000) 413-446. | MR | Zbl
, , ,[10] Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Rev. 34 (1992) 45-81. | MR | Zbl
, , ,[11] On the theory of superconductivity, Soviet Phys. JETP 20 (1950) 1064-1082.
, ,[12] The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal. 30 (1999) 341-359. | MR | Zbl
, ,[13] Semi-Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, 1336, Springer-Verlag, 1988. | MR | Zbl
,[14] Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells, J. Funct. Anal. 138 (1996) 40-81. | MR | Zbl
, ,[15] Magnetic bottles in connection with superconductivity, J. Funct. Anal. 185 (2001) 604-680. | MR | Zbl
, ,[16] The first eigenvalue of Ginzburg-Landau operator, in: , (Eds.), Differential Equations and Applications, International Press, 1997, pp. 215-226. | MR | Zbl
, ,[17] Gauge invariant eigenvalue problems in R2 and in R2+, Trans. Amer. Math. Soc. 352 (2000) 1247-1276. | MR | Zbl
, ,[18] Eigenvalue problems of Ginzburg-Landau operator in bounded domains, J. Math. Phys. 40 (1999) 2647-2670. | MR | Zbl
, ,[19] Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Phys. D 127 (1999) 73-104. | MR | Zbl
, ,[20] Surface nucleation of superconductivity in 3-dimension, J. Differential Equations 168 (2000) 386-452. | MR | Zbl
, ,[21] Surface nucleation of superconductivity, Methods and Applications of Analysis 8 (2001) 279-300. | MR | Zbl
, ,[22] Onset of superconductivity in decreasing fields, Phys. Lett. 6 (5) (1963) 306-308.
, ,[23] Type II Superconductivity, Pergamon Press, Oxford, 1969.
, , ,[24] Introduction to Superconductivity, McGraw-Hill, New York, 1975.
,