A rigorous derivation of a free-boundary problem arising in superconductivity

We study the Ginzburg-Landau energy of superconductors submitted to a possi bly nonuniform magnetic field, in the limit of a large Ginzburg-Landau para meter re. We prove that the induced magnetic fields associated to minimizer s of the energy-functional converge as kappa --> + infinity to the solution of a free-boundary problem. This free-boundary problem has a nontrivial so lution only when the applied magnetic field is of the order of the "first c ritical field", i.e. of the order of log kappa. In other cases, our results are contained in those we had previously obtained [15, 16, 14]. We also de rive a convergence result for the density of vortices. (C) 2000 Editions sc ientifiques et medicales Elsevier SAS.