The distribution of surface superconductivity along the boundary: On a conjecture of X. B. Pan

We consider the Ginzburg-Landau model of superconductivity in two dimensions in the large. limit. For applied magnetic fields weaker than the onset field H-C3 but greater than H-C2 it is well known that the superconductivity order parameter decays exponentially fast away from the boundary. It has been conjectured by X. B. Pan that this surface superconductivity solution converges pointwise to a constant along the boundary. For applied fields that are in some sense between H-C2 and H-C3, we prove that the solution indeed converges to a constant but in a much weaker sense.