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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

Abstract

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.

Keywords

Singular Point Variational Problem Thin Strip Suitable Sense Embed Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: koby@leeor.technion.ac.ilIL
  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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