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

Étienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)561-592
Number of pages32
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Issue number4
StatePublished - May 2000

ASJC Scopus subject areas

  • General Mathematics


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