Vortex-filaments for inhomogeneous superconductors in three dimensions

In this paper, the asymptotic behavior of solutions to the Ginzburg–Landau system of inhomogeneous superconductivity in three dimensions was studied with an applied magnetic field |hex|=O(|lnε|). We show that the limiting singularities set is 1-dimensional rectifiable, which mean curvature was also given. In particular, we study the effect of the inhomogeneous term to vortex-filaments.