The ground state energy of the three-dimensional Ginzburg–Landau model in the mixed phase

We consider the Ginzburg–Landau functional defined over a bounded and smooth three-dimensional domain. Supposing that the strength of the applied magnetic field varies between the first and second critical fields, in such a way that HC1≪H≪HC2, we estimate the ground state energy to leading order as the Ginzburg–Landau parameter tends to infinity.