TY - JOUR

T1 - A rigorous derivation of a free-boundary problem arising in superconductivity

AU - Sandier, Étienne

AU - Serfaty, Sylvia

PY - 2000/5

Y1 - 2000/5

N2 - 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.

AB - 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.

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U2 - 10.1016/S0012-9593(00)00122-1

DO - 10.1016/S0012-9593(00)00122-1

M3 - Article

AN - SCOPUS:0003275448

SN - 0012-9593

VL - 33

SP - 561

EP - 592

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 4

ER -