Ebook: Variational Methods: Proceedings of a Conference Paris, June 1988

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.

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Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
The (Non)Continuity of Symmetric Decreasing Rearrangement....Pages 3-16
Counting Singularities in Liquid Crystals....Pages 17-35
Relaxed Energies for Harmonic Maps....Pages 37-52
Topological results on Fredholm maps and application to a superlinear differential equation....Pages 53-59
Existence Results for some Quasilinear Elliptic Equations....Pages 61-76
A New Setting For Skyrme’s Problem....Pages 77-93
Relative Category and The Calculus of Variations....Pages 95-104
Point and Line Singularities in Liquid Crystals....Pages 105-113
The Variety of Configurations of Static Liquid Crystals....Pages 115-131
Lagrange Multipliers, Morses Indices and Compactness....Pages 133-159
Elliptic equations with critical growth and Moser’s inequality....Pages 161-184
Evolution equations with discontinuous nonlinearities and non-convex constraints....Pages 185-196
Nonlinear Variational Two-Point Boundary Value Problems....Pages 197-208
Some Relative Isoperimetric Inequalities and Applications to Nonlinear Problems....Pages 209-218
Front Matter....Pages 219-235
Approximation in Sobolev Spaces between two manifolds and homotopy groups....Pages 237-237
The “magic” of Weitzenb?ck formulas....Pages 239-249
A Remark on Minimal Surfaces with Corners....Pages 251-271
Convergence of Minimal Submanifolds to a Singular Variety....Pages 273-282
Front Matter....Pages 283-296
Harmonic Diffeomorphisms between Riemannian Manifolds....Pages 297-307
Calibrations and New Singularities in Area-minimizing Surfaces: A Survey....Pages 237-237
Harmonic Maps with Free Boundaries....Pages 309-318
Global existence and partial regularity results for the evolution of harmonic maps....Pages 319-327
Front Matter....Pages 329-342
Multiple periodic trajectories in a relativistic gravitational field....Pages 343-357
Periodic Solutions of Some Problems of 3-Body Type....Pages 359-369
Periodic Solutions of Dissipative Dynamical Systems....Pages 371-371
Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field....Pages 373-381
Morse Theory for Harmonic Maps....Pages 383-394
Morse Theory and Existence of Periodic Solutions of Elliptic Type....Pages 395-411
Periodic Solutions of a Nonlinear Second Order System....Pages 413-429
Existence of Multiple Brake Orbits for a Hamiltonian System....Pages 431-446
Back Matter....Pages 447-453
....Pages 455-468