The influence of magnetic steps on bulk superconductivity

We study the distribution of bulk superconductivity in presence of an applied magnetic field, supposed to be a step function, modeled by the Ginzburg-Landau theory. Our results are valid for the minimizers of the two-dimensional Ginzburg-Landau functional with a large Ginzburg-Landau parameter and with an applied magnetic field of intensity comparable with the Ginzburg-Landau parameter.