Boundary concentration for eigenvalue problems related to the onset of superconductivity

Communications in Mathematical Physics

Volumn 210, Issue 2, 2000, Pages 413-446

  Del Pino, Manuel ^a   Felmer, Patricio L ^a   Sternberg, Peter ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034348882     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050786     Document Type: Article

References (24)

1. [ADN] Agmon, S., Douglis, A. and Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. C.P.A.M. 17, 35-92 (1964)
2. [BPT] Bauman, P., Phillips, D. and Tang, Q.: Stable nucleation for the Ginzburg - Landau system with an applied magnetic field. Arch. Rat. Mech. Anal. 142, 1-43 (1998)
3. [BRI] Berger, J. and Rubinstein, J.: Formation of topological defects in thin superconducting rings. Phil. Trans. R. Soc. Lond. A 355, 1969-1978 (1997)
4. [BR2] Berger, J. and Rubinstein, J.: Bifurcation analysis for phase transitions in superconducting rings with nonuniform thickness. SIAM J. Appl. Math. 58, 103-121 (1998)
5. [BS] Bernoff, A. and Sternberg, P.: Onset of superconductivity in decreasing fields for general domains. J. Math. Phys. 39, 1272-1284 (1998)
6. 2AN 26, 235-287 (1992)
7. [BH] Bolley, C. and Helffer, B.: An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material. Ann. Inst. H. Poincaré: Phys. Theor. 58, 189-233 (1993)
8. [BRPVM] Bruyndoncx, V., Rodrigo, J.G., Puig, T. Van Look, L. Moshchalkov, V.V.: Giant vortex state in perforated aluminum microsquares. Preprint
9. [BGRW] Buisson, O., Gandit, P., Rammal, R., Wang, Y.Y. and Pannetier, B.: Magnetization oscillations of a superconducting disk. Phys. Lett. A 150, 36-42 (1990)
10. [C1] Chapman, S.J.: Nucleation of superconductivity in decreasing fields, I. Euro. J. Appl. Math. 5, 449-468 (1994)
11. [C2] Chapman, S.J.: Nucleation of superconductivity in decreasing fields, II. Euro. J. Appl. Math. 5, 469-494 (1994)
12. [DH] Dauge, M. and Helffer, B.: Eigenvalues variation I, Neumann problem for Sturm-Liouville operators. J.D.E. 104, 243-262 (1993)
13. [DGP] Du, Q., Gunzburger, M.D. and Peterson, J.S.: Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Review 34, 45-81 (1992)
14. [GL] Ginzburg, V.L. and Landau, L.D.: On the theory of superconductivity. J.E.T.P. 20, 1064 (1950)
15. [GP] Giorgi, T. and Phillips, D.: The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model. SIAM J. Math. Anal. 30, 341-359 (1999)
16. [JRS] Jadallah, H. Rubinstein, J. and Sternberg, P.: Phrase transition curves for mesoscopic superconducting samples. Phys. Rev. Let. 82 14, 2935-2938 (1999)
17. [LS] Levitan, B.M. and Sargsjan, I.S.: Sturm-Liouville and Dirac Operators. Mathematics and Its Applications (Soviet Series), Vol. 59, Amsterdam: Kluwer Academic Publications, 1991
18. + Preprint
19. [LP2] Lu, K. and Pan, X.B.: Eigenvalue problems of Ginzburg-Landau operator in bounded domains. J. Math. Phys. 40, 2647-670 (1999)
20. [LP3] Lu, K. and Pan, X.B.: Estimates of the upper critical external magnetic field for the Ginzburg-Landau equations: Physica D 127, 73-104 (1999)
21. [MK] Millman, M.H. and Keller, J.B.: Perturbation theory of nonlinear boundary value problems. J. Math. Phys. 10, 342-61 (1969)
22. [MGSJQVB] Moschchalkov, V.V., Gielen, L. Strunk, C., Jonckheere, R., Qiu, X., Van Haesendonck, C. and Bruynseraede, Y.: Effect of sample topology on the critical fields of mesoscopic superconductors. Nature 373, 319-322 (January 1995)
23. [O] Odeh, F.: Existence and bifurcation theorems for the Ginzburg-Landau equations. J. Math. Phys. 8, 2351-357 (1967)
24. [SD] Saint-James, D. and de Gennes, P.G.: Onset of superconductivity in decreasing fields. Phys. Lett. 7, 306-308 (1963)