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Vortex pinning with bounded fields for the Ginzburg-Landau equation. (English) Zbl 1040.35108
From the authors’ abstract: The vortex pinning in solutions to the Ginzburg-Landau equation is investigated. The coefficient, \(a(x)\), in the Ginzburg-Landau free energy modelling non-uniform superconductivity is nonnegative and is allowed to vanish at a finite number of points. For a sufficiently large applied magnetic field and for all sufficiently large values of the Ginzburg-Landau parameter \(k=1/\varepsilon\), it is shown that minimizers have nontrivial vortex structures. It is proved, also, the existence of local minimizers exhibiting arbitrary vortex patterns pinned near the zeros of \(a(x)\).

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanical studies of superconductors
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