Singular limits for thin film superconductors in strong magnetic fields

We consider singular limits of the three-dimensional Ginzburg–Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale ε>0, and we consider the simultaneous limit as the thickness ε→0 and the Ginzburg–Landau parameter κ→∞. We assume that the applied field is strong (on the order of ε −1 in magnitude) in its components tangential to …