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Variational Methods

Proceedings of a Conference Paris, June 1988

  • Conference proceedings
  • © 1990

Overview

Editors:
  1. Henri Berestycki

    1. Mathématiques, Université Pierre et Marie Curie, Paris Cedex 05, France

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  2. Jean-Michel Coron

    1. Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, Orsay Cedex, France

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  3. Ivar Ekeland

    1. CEREMADE, Université de Paris IX-Dauphine, Paris Cedex 16, France

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 4)

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Table of contents (33 papers)

  1. Front Matter

    Pages i-ix
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  2. Partial Differential Equations and Mathematical Physics

    1. Front Matter

      Pages 1-1
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    2. The (Non)Continuity of Symmetric Decreasing Rearrangement

      • Frederick J. Almgren Jr., Elliott H. Lieb
      Pages 3-16

    3. Counting Singularities in Liquid Crystals

      • Frederick J. Almgren Jr., Elliott H. Lieb
      Pages 17-35

    4. Relaxed Energies for Harmonic Maps

      • F. Bethuel, H. Brezis, J. M. Coron
      Pages 37-52

    5. Topological results on Fredholm maps and application to a superlinear differential equation

      • Vittorio Cafagna
      Pages 53-59

    6. Existence Results for some Quasilinear Elliptic Equations

      • Henrik Egnell
      Pages 61-76

    7. A New Setting For Skyrme’s Problem

      • Maria J. Esteban
      Pages 77-93

    8. Relative Category and The Calculus of Variations

      • G. Fournier, M. Willem
      Pages 95-104

    9. Point and Line Singularities in Liquid Crystals

      • Robert M. Hardt
      Pages 105-113

    10. The Variety of Configurations of Static Liquid Crystals

      • Robert Hardt, David Kinderlehrer, Fang Hau Lin
      Pages 115-131

    11. Existence of Multiple Solutions of Semilinear Elliptic Equations in R N

      • Yanyan Li
      Pages 133-159

    12. Lagrange Multipliers, Morses Indices and Compactness

      • P. L. Lions
      Pages 161-184

    13. Elliptic equations with critical growth and Moser’s inequality

      • J. B. McLeod, L. A. Peletier
      Pages 185-196

    14. Evolution equations with discontinuous nonlinearities and non-convex constraints

      • A. Marino, C. Saccon
      Pages 197-208

    15. Nonlinear Variational Two-Point Boundary Value Problems

      • J. Mawhin
      Pages 209-218

    16. Some Relative Isoperimetric Inequalities and Applications to Nonlinear Problems

      • Filomena Pacella
      Pages 219-235

  3. Partial Differential Equations and Problems in Geometry

    1. Front Matter

      Pages 237-237
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    2. Approximation in Sobolev Spaces between two manifolds and homotopy groups

      • Fabrice Bethuel
      Pages 239-249

    3. The “magic” of Weitzenböck formulas

      • Jean-Pierre Bourguignon
      Pages 251-271
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Keywords

About this book

In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien­ tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat­ ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap­ plications from various domains of sciences and industrial applica­ tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat­ ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics.

Editors and Affiliations

  • Mathématiques, Université Pierre et Marie Curie, Paris Cedex 05, France

    Henri Berestycki

  • Département de Mathématiques, Bâtiment 425, Université de Paris-Sud, Orsay Cedex, France

    Jean-Michel Coron

  • CEREMADE, Université de Paris IX-Dauphine, Paris Cedex 16, France

    Ivar Ekeland

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