The Ginzburg-Landau order parameter near the second critical field

In Ginzburg-Landau Theory of superconductivity, the density and location of the superconducting electrons are measured by a complex-valued wave function, the order parameter. In this paper, when the intensity of the applied magnetic field is close to the second critical field, and when the order parameter minimizes the Ginzburg-Landau functional defined over a two dimensional domain, the leading order approximation of its $L^2$-norm in `small' squares is given as the Ginzburg-Landau parameter tends to infinity.