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The configuration (aj) minimizes the renormalized energy W

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

Abstract

In Section 1.4 we have introduced the renormalized energy W = W(a,d,g) for a general configuration of points (ai),1≤ i ≤ n, with associated integers d i Z such that \( \sum\nolimits_{{i = 1}}^n {{d_i} = d} \) Throughout this chapter we consider only configurations consisting of exactly d distinct points in G, each one associated to d i =+1.

Keywords

Unique Minimizer Theorem VIII Harmonic Conjugate Hopf Differential Renormalize Energy 
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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