Vortex pinning with bounded fields for the Ginzburg-Landau equation

We investigate vortex pinning in solutions to the Ginzburg-Landau equation. The coefficient, a (x), in the Ginzburg-Landau free energy modeling 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 kappa = 1/epsilon, we show that minimizers have nontrivial vortex structures. We also show the existence of local minimizers exhibiting arbitrary vortex patterns, pinned near the zeros of a (x). (C) 2003 Editions scientifiques et medicales Elsevier SAS.