Local minimizers for the Ginzburg-Landau energy near critical magnetic field. I. (English) Zbl 0944.49007

The paper deals with the study of local minimizers of the Ginzburg-Landau functional with high parameter. This problem is motivated by the behaviour of the energy of a cylindrical superconductor in a prescribed exterior magnetic field and by the fact that the stationary states of such a superconductor are the critical points of the Ginzburg-Landau functional, among which the stable states are the local minimizers. The proofs are based on refined powerful energy estimates and the methods employed in the paper offer an interesting treatment, with large perspectives, of various superconductivity problems with free boundary behaviour.


49J35 Existence of solutions for minimax problems
49K20 Optimality conditions for problems involving partial differential equations
35J20 Variational methods for second-order elliptic equations
82D55 Statistical mechanics of superconductors
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[1] 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] Phys. 107 pp 649– (1986)
[4] DOI: 10.1007/BF00375695 · Zbl 0809.35019 · doi:10.1007/BF00375695
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