Variational Methods: Proceedings of a Conference Paris, June 1988

Description

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 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 Existence of Multiple Solutions of Semilinear Elliptic Equations in R N ....Pages 133-159 Lagrange Multipliers, Morses Indices and Compactness....Pages 161-184 Elliptic equations with critical growth and Moser’s inequality....Pages 185-196 Evolution equations with discontinuous nonlinearities and non-convex constraints....Pages 197-208 Nonlinear Variational Two-Point Boundary Value Problems....Pages 209-218 Some Relative Isoperimetric Inequalities and Applications to Nonlinear Problems....Pages 219-235 Front Matter....Pages 237-237 Approximation in Sobolev Spaces between two manifolds and homotopy groups....Pages 239-249 The “magic” of Weitzenböck formulas....Pages 251-271 A Remark on Minimal Surfaces with Corners....Pages 273-282 Extremal Surfaces of Mixed Type in Minkowski Space R n+1 ....Pages 283-296 Convergence of Minimal Submanifolds to a Singular Variety....Pages 297-307 Front Matter....Pages 237-237 Harmonic Diffeomorphisms between Riemannian Manifolds....Pages 309-318 Surfaces of Minimal Area Supported by a Given Body in ℝ 3 ....Pages 319-327 Calibrations and New Singularities in Area-minimizing Surfaces: A Survey....Pages 329-342 Harmonic Maps with Free Boundaries....Pages 343-357 Global existence and partial regularity results for the evolution of harmonic maps....Pages 359-369 Front Matter....Pages 371-371 Multiple periodic trajectories in a relativistic gravitational field....Pages 373-381 Periodic Solutions of Some Problems of 3-Body Type....Pages 383-394 Periodic Solutions of Dissipative Dynamical Systems....Pages 395-411 Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field....Pages 413-429 Morse Theory for Harmonic Maps....Pages 431-446 Morse Theory and Existence of Periodic Solutions of Elliptic Type....Pages 447-453 Periodic Solutions of a Nonlinear Second Order System....Pages 455-468 Existence of Multiple Brake Orbits for a Hamiltonian System....Pages 469-477 Back Matter....Pages 478-478