A branched transport limit of the Ginzburg-Landau functional

Sergio Conti, Michael Goldman, Felix Otto, Sylvia Serfaty

Research output: Contribution to journalArticlepeer-review


We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via -convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.

Original languageEnglish (US)
Pages (from-to)317-375
Number of pages59
JournalJournal de l'Ecole Polytechnique - Mathematiques
StatePublished - 2018


  • Branched transportation
  • Gamma convergence
  • Ginzburg-Landau
  • Pattern formation
  • Type-I superconductors

ASJC Scopus subject areas

  • General Mathematics


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