On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

Leonid Berlyand, Dmitry Golovaty, Oleksandr Iaroshenko, Volodymyr Rybalko

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2 Scopus citations


We consider a two-dimensional Ginzburg–Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg–Landau parameter vs. hole radius) is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg–Landau problems in the classes of S1-valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.

Original languageEnglish (US)
Pages (from-to)1317-1347
Number of pages31
JournalJournal of Differential Equations
Issue number2
StatePublished - Jan 15 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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