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Birkhäuser

Ginzburg-Landau Vortices

  • Book
  • © 1994

Overview

Authors:
  1. Fabrice Bethuel

    1. Laboratoire d’Analyse Numérique, Université Paris-Sud, Orsay Cedex, France

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  2. Haïm Brezis

    1. Analyse Numérique Université Pierre et Marie Curie, Paris Cedex 05, France
      Department of Mathematics, Rutgers University, New Brunswick, USA

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  3. Frédéric Hélein

    1. CMLA, ENS-Cachan, Cachan Cedex, France

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 13)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Energy estimates for S1-valued maps

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 1-30

  3. A lower bound for the energy of S1-valued maps on perforated domains

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 31-41

  4. Some basic estimates for u∈

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 42-47

  5. Towards locating the singularities: bad discs and good discs

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 48-51

  6. An upper bound for the energy of u∈ away from the singularities

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 52-56

  7. u∈n converges: u★ is born!

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 57-64

  8. u★ coincides with THE canonical harmonic map having singularities (a j )

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 65-75

  9. The configuration (aj) minimizes the renormalized energy W

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 76-99

  10. Some additional properties of u∈

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 100-106

  11. Non-minimizing solutions of the Ginzburg-Landau equation

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 107-136

  12. Open problems

    • Fabrice Bethuel, Haïm Brezis, Frédéric Hélein
    Pages 137-141

  13. Back Matter

    Pages 142-162
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Keywords

Reviews

"The three authors are well-known excellent specialists in nonlinear functional analysis and partial differential equations and the material presented in the book covers some of their recent and original results. The book is written in a very clear and readable style with many examples."

--ZAA

"...the book gives a very stimulating account of an interesting minimization problem. It can be a fruitful source of ideas for those who work through the material carefully."

--ZAMP

Authors and Affiliations

  • Laboratoire d’Analyse Numérique, Université Paris-Sud, Orsay Cedex, France

    Fabrice Bethuel

  • Analyse Numérique Université Pierre et Marie Curie, Paris Cedex 05, France

    Haïm Brezis

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Haïm Brezis

  • CMLA, ENS-Cachan, Cachan Cedex, France

    Frédéric Hélein

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