Energy estimate for the type-II superconducting film

Abstract

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high kappa, placed in an applied magnetic field h(ex) when h(ex) is of the order of the "first critical field", i.e. of the order of vertical bar ln epsilon vertical bar. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.