We study the Ginzburg-Landau energy of superconductors submitted to a possibly non-uniform magnetic field, in the limit of a large Ginzburg-Landau parameter κ . We prove that the induced magnetic fields associated to minimizers of the energy-functional converge as κ→+∞ to the solution of a free-boundary problem. This free-boundary problem has a nontrivial solution only when the applied magnetic field is of the order of the "first critical field", i.e. of the order of logκ . In other cases, our results are contained in those we had previously obtained [15, 16, 14]. We also derive a convergence result for the density of vortices.
|Original language||English (US)|
|Number of pages||32|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - May 2000|
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