Vortex-filaments pinning for inhomogeneous Ginzburg–Landau equations

In this paper, the structure of vortices of the Ginzburg–Landau system with impurity in higher dimensions was studied. This functional has been proposed as a model for vortex-pinning. We show that vortices are localized near the set of minimum of impurity. This is the pinning phenomenon predicted in the physics literature. It was also proven that the limiting vortices is (N-2)(N-2)-dimensional rectifiable set.