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Topological methods for the Ginzburg-Landau equations

1998; Elsevier BV; Volume: 77; Issue: 1 Linguagem: Inglês

10.1016/s0021-7824(98)80064-0

ISSN

1776-3371

Autores

Luís Almeida, Fabrice Béthuel,

Tópico(s)

Geometric Analysis and Curvature Flows

Resumo

We consider the complex-valued Ginzburg-Landau equation on a two-dimensional domain Ω, with boundary data g, such that ∥g∥ = 1, −Δu=1ϵ2u(1−∥u∥2),u=g. We develop a variational framework for this equation: in particular we show that the topology of the level sets is related to a finite dimensional functional, the renormalized energy. As an application, we prove a multiplicity result of solutions for the equation, when ε is small and the winding number of g is larger or equal to 2.

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