Serfaty, Sylvia Local minimizers for the Ginzburg-Landau energy near critical magnetic field. I. (English) Zbl 0944.49007 Commun. Contemp. Math. 1, No. 2, 213-254 (1999). 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. Reviewer: Vicentiu D.Rădulescu (Craiova) Cited in 3 ReviewsCited in 45 Documents MSC: 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 Keywords:minimization problem; Ginzburg-Landau theory; renormalized energy; asymptotic study PDF BibTeX XML Cite \textit{S. Serfaty}, Commun. Contemp. Math. 1, No. 2, 213--254 (1999; Zbl 0944.49007) Full Text: DOI OpenURL References: [1] Phys. JETP 5 pp 1174– (1957) [2] DOI: 10.1016/S0021-7824(98)80064-0 · Zbl 0904.35023 [3] Phys. 107 pp 649– (1986) [4] DOI: 10.1007/BF00375695 · Zbl 0809.35019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.