Vortices for a variational problem related to superconductivity. (English) Zbl 0842.35119

Summary: We study minimizers of Ginzburg-Landau functionals, which depend on a parameter \(\varepsilon\). These functionals appear in superconductivity and two dimensional abelian Higgs models. We study the asymptotic limit, as \(\varepsilon \to 0\), of minimizers and show that the limiting configuration has vortices, which have topological degree one.


35Q60 PDEs in connection with optics and electromagnetic theory
35A15 Variational methods applied to PDEs
82D55 Statistical mechanics of superconductors
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