The ground state energy of the three dimensional Ginzburg-Landau functional. Part~II: Surface regime

We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that superconductivity should be essentially restricted to a region near the boundary. We prove that the expected region does indeed carry superconductivity. Furthermore, we give precise energy estimates valid also in the regime around the second critical field which display the transition from bulk superconductivity to surface superconductivity.