Eigenvalue problems of Ginzburg-Landau operator in bounded domains

Journal of Mathematical Physics

Volumn 40, Issue 6, 1999, Pages 2647-2670

  Lu, Kening ^a   Pan, Xing Bin ^b  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033147659     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532721     Document Type: Article

References (20)

1. K. Lu and X.-B. Pan, "Estimates of upper critical external magnetic field for the Ginzburg-Landau equation," Physica D 127, 73-104 (1999).
2. D. Saint-James and P. de Gennes, "Onset of superconductivity in decreasing fields," Phys. Lett. 7, 306-308 (1963).
3. S. J. Chapman, "Nucleation of superconductivity in decreasing fields, 1, 2," Eur. J. Appl. Math. 5, 449-468 (1994); 5, 469-494 (1994).
4. S. J. Chapman, "Nucleation of superconductivity in decreasing fields, 1, 2," Eur. J. Appl. Math. 5, 449-468 (1994); 5, 469-494 (1994).
5. +," Trans. Am. Math. Soc. (to be published).
6. V. Ginzburg and L. Landau, "On the theory of superconductivity," Sov. Phys. JETP 20, 1064-1082 (1950).
7. P. De Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966).
8. P. Bauman, D. Phillips, and Q. Tang, "Stable nucleation for the Ginzburg-Landau system with an applied magnetic field," Arch. Ration. Mech. Anal. 142, 1-43 (1998).
9. F. Bethuel, H. Brézis, and F. Hélein, Ginzburg-Landau Vortices (Birkhöuser, Boston, 1994).
10. F. Bethuel and T. Riviére, "Vortices for a variational problem related to superconductivity," Ann. Inst. Henri Poincaré Anal. Non Linéaire 12, 243-303 (1995).
11. A. Bernoff and P. Sternberg, "Onset of superconductivity in decreasing fields for general domains," J. Math. Phys. 39, 1272-1284 (1998).
12. S. J. Chapman, S. D. Howison, and J. R. Ockendon, "Macroscopic models for superconductivity," SIAM (Soc. Ind. Appl. Math.) Rev. 34, 529-560 (1992).
13. S. Chanillo and M. Kiessling, "Symmetry of solutions of Ginzburg-Landau equations," Comp. Rend. Acad. Sci., Paris, 32, 1023-1026 (1995).
14. Q. Du, M. Gunzburger, and J. Peterson, "Analysis and approximation of the Ginzburg-Landau model of superconductivity," SIAM (Soc. Ind. Appl. Math.) Rev. 34, 45-81 (1992).
15. A. Jaffe and C. Taubes, Vortices and Monopoles (Birkhäuser, Boston, 1980).
16. F.-H. Lin, "Solutions of Ginzburg-Landau equations and critical points of the renormalized energy," Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, 599-622 (1995).
17. F.-H. Lin and T.-C. Lin, "Minimax solutions of the Ginzburg-Landau equations," Selecta Math. (N.S.) 3, 99-113 (1997).
18. K. Lu and X.-B. Pan, "Ginzburg-Landau equation with DeGennes boundary condition," J. Diff. Eqns. 129, 136-165 (1996).
19. P. Mironescu, "On the stability of radial solutions of the Ginzburg-Landau equations," J. Funct. Anal. 130, 334-347 (1995).
20. M. Struwer, "On the asymptotical behavior of minimizers of the Ginzburg-Landau model in 2-dimensions," J. Diff. Eqns. 7, 1613-1627 (1994).