Variational Methods: Proceedings of a Conference Paris, June 1988

ISBN-13: 9781475710823 / Angielski / Miękka / 2012 / 478 str.

Berestycki

Opis

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.

Spis treści

I: Partial Differential Equations and Mathematical Physics.- 1. The (Non)continuity of Symmetric Decreasing Rearrangement.- 2. Counting Singularities in Liquid Crystals.- 3. Relaxed Energies for Harmonic Maps.- 4. Topological Results on Fredholm Maps and Application to a Superlinear Differential Equation.- 5. Existence Results for Some Quasilinear Elliptic Equations.- 6. A New Setting for Skyrme’s Problem.- 7. Relative Category and the Calculus of Variations.- 8. Point and Line Singularities in Liquid Crystals.- 9. The Variety of Configurations of Static Liquid Crystals.- 10. Existence of Multiple Solutions of Semilinear Elliptic Equations in RN.- 11. Lagrange Multipliers, Morses Indices and Compactness.- 12. Elliptic Equations with Critical Growth and Moser’s Inequality.- 13. Evolution Equations with Discontinuous Nonlinearities and Non-Convex Constraints.- 14. Nonlinear Variational Two-Point Boundary Value Problems.- 15. Some Relative Isoperimetric Inequalities and Applications to Nonlinear Problems.- II: Partial Differential Equations and Problems in Geometry.- 16. Approximation in Sobolev Spaces Between Two Manifolds and Homotopy Groups.- 17. The “Magic” of Weitzenböck Formulas.- 18. A Remark on Minimal Surfaces with Corners.- 19. Extremal Surfaces of Mixed Type in Minkowski Space Rn+1.- 20. Convergence of Minimal Submanifolds to a Singular Variety.- 21. Harmonic Diffeomorphisms Between Riemannian Manifolds.- 22. Surfaces of Minimal Area Supported by a Given Body in ?3.- 23. Calibrations and New Singularities in Area-Minimizing Surfaces: A Survey.- 24. Harmonic Maps with Free Boundaries.- 25. Global Existence of Partial Regularity Results for the Evolution of Harmonic Maps.- III: Hamiltonian Systems.- 26. Multiple Periodic Trajectories in a Relativistic Gravitational Field.- 27. Periodic Solutions of Some Problems of 3-Body Type.- 28. Periodic Solutions of Dissipative Dynamical Systems.- 29. Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field.- 30. Morse Theory for Harmonic Maps.- 31. Morse Theory and Existence of Periodic Solutions of Elliptic Type.- 32. Periodic Solutions of a Nonlinear Second Order System.- 33. Existence of Multiple Brake Orbits for a Hamiltonian System.