Variational Methods

1. Front Matter

   Pages i-ix

   PDF

2. Partial Differential Equations and Mathematical Physics

   1. Front Matter

      Pages 1-1

      PDF

   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

      PDF

   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

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.

• Boundary value problem
• Mathematica
• Scope
• Sobolev space
• Volume
• differential equation
• dynamical systems
• equation
• framework
• geometry
• hamiltonian system
• mechanics
• online
• partial differential equation
• themes
• partial differential equations

• 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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