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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 \(a(x)\).

35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanical studies of superconductors
Full Text: DOI Numdam EuDML
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