  We consider the two-dimensional Ginzburg-Landau functional with constant
applied magnetic field. For applied magnetic fields close to the second
critical field $H_{C_2}$ and large Ginzburg-Landau parameter, we provide
leading order estimates on the energy of minimizing configurations. We obtain a
fine threshold value of the applied magnetic field for which bulk
superconductivity contributes to the leading order of the energy. Furthermore,
the energy of the bulk is related to that of the Abrikosov problem in a
periodic lattice. A key ingredient of the proof is a novel $L^\infty$-bound
which is of independent interest.
