Local minimizers for the Ginzburg-Landau energy near critical magnetic field. II. (English) Zbl 0964.49005

As in Part I [Commun. Contemp. Math. 1, No. 3, 295-333 (1999; Zbl 0944.49007)] the author studies here local minimizers of the Ginzburg-Landau energy functional (depending on \( \kappa \to + \infty)\) over some domain \( \Omega \) for superconductors in a prescribed magnetic field \( h_{ex} \). Assuming that the domain \( \Omega \) has the form of a disc the author finds and describes stable solutions of the associated equations and shows how vortices appear as \( h_{ex} \) is raised from the first critical field \( H_{c_1} \). He also studies the limit \( \kappa \to + \infty \) for \( h_{ex} = H_{c_1} \) and proves that the limiting magnetic field in the superconductor satisfies the London-type equation.
In the paper some results presented in Part I are proved. The extensive appendix contains technical details concerning the proofs.
Some open problems are posed.


49J35 Existence of solutions for minimax problems
82D55 Statistical mechanics of superconductors
49K20 Optimality conditions for problems involving partial differential equations
35J20 Variational methods for second-order elliptic equations


Zbl 0944.49007
Full Text: DOI


[1] Abrikosov A., Soviet Phys. JETP 5 pp 1174– (1957)
[2] DOI: 10.1016/S0021-7824(98)80064-0 · Zbl 0904.35023 · doi:10.1016/S0021-7824(98)80064-0
[3] DOI: 10.1007/BF01191614 · Zbl 0834.35014 · doi:10.1007/BF01191614
[4] DOI: 10.1007/BF01205490 · Zbl 0608.58016 · doi:10.1007/BF01205490
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