The distribution of 3D superconductivity near the second critical field (Q2821965)

This paper deals with the asymptotic analysis of minimizers of the Ginzburg-Landau energy with uniform magnetic field. The main result of this paper establishes a formula for the distribution of the \(L^2\)-norm of the minimizing complex-valued function. This formula is valid when the Ginzburg-Landau parameter is large and the magnetic field is close and strictly below the second critical field. The proofs combine elliptic estimates, energy estimates and asymptotics of the Ginzurg-Landau energy in cubes with small lengths.