Non-homogeneous magnetic permeability and magnetic steps within the Ginzburg-Landau model

摘要

We study the Ginzburg-Landau model in the frame of non-homogeneous magnetic permeabilities and non-homogeneous applied magnetic fields. We establish a continuity result with respect to the applied magnetic field and the magnetic permeability coefficient, thereby motivating the consideration of a discontinuous magnetic field/permeability within the sample. We then study the model in the regime of a large Ginzburg-Landau parameter and strong applied magnetic fields. The discontinuity of the magnetic permeability term leads to regularity issues, which we handle by energy arguments.