Archive for Rational Mechanics and Analysis

, Volume 160, Issue 4, pp 309–324 | Cite as

Variational Problems¶on Multiply Connected Thin Strips II:¶Convergence of the Ginzburg-Landau

  • Jacob Rubinstein
  • Michelle Schatzman


Let M be a planar embedded graph whose arcs meet transversally at the vertices; Let ?(M) be a strip-shaped domain around M, of width M except in a neighborhood of the singular points. Assume that the boundary of ?(M) is smooth. We consider the Ginzburg-Landau energy functional for superconductivity on ?(M). We prove that its minimizers converge in a suitable sense to the minimizers of a simpler functional on M. The supercurrents in ?(M) are shown to converge to one-dimensional currents in M.


Singular Point Variational Problem Thin Strip Suitable Sense Embed Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jacob Rubinstein
    • 1
  • Michelle Schatzman
    • 2
  1. 1.Department of Mathematics¶Technion¶Haifa 32000, Israel¶e-mail:
  2. 2.MAPLY, CNRS¶et Université Claude Bernard – Lyon 1¶21 Avenue Claude Bernard¶69622 Villeurbanne Cedex, France¶e-mail: schatz@maply.univ-lyon1.frFR

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