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Non-minimizing solutions of the Ginzburg-Landau equation

  • Fabrice Bethuel
  • Haïm Brezis
  • Frédéric Hélein
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 13)

Abstract

Throughout this chapter, we analyze the behavior as \( \varepsilon \to 0 \) of solutions vε of the Ginzburg-Landau equation:
$$ - \Delta {v_\varepsilon } = \frac{1}{{{\varepsilon ^2}}}{v_\varepsilon }\left( {1 - {{\left| {{v_\varepsilon }} \right|}^2}} \right)\quad in G $$
(1)
,
$$ {v_\varepsilon } = g\quad on\,\partial G $$
(2)
.

Keywords

Universal Constant Sobolev Embedding Associate Linear Problem Smooth Harmonic Function 41rd Fori 
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 Science+Business Media New York 1994

Authors and Affiliations

  • Fabrice Bethuel
    • 1
  • Haïm Brezis
    • 2
    • 3
  • Frédéric Hélein
    • 4
  1. 1.Laboratoire d’Analyse NumériqueUniversité Paris-SudOrsay CedexFrance
  2. 2.Analyse Numérique Université Pierre et Marie CurieParis Cedex 05France
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA
  4. 4.CMLA, ENS-CachanCachan CedexFrance

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