This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Table of Contents
1. Categories of Dynamical Models 2. Almost Universal Maps and the Almost Fixed Point Property 3. On the Natural Approach to Flow Problems 4. Differential Geometry and Lagrangian Formalism 5. The Geometry of Bicharacteristics and Stability of Solvability 6. The Simplest Nonlinear Yang-Mills Theory that Works 7. Euler, Morse, and the Calculus of Variations 8. The Birth and Early Developments of Pade Approximants 9. On the Approximation of Solutions of Quasivariatlonal Inequalities with Application to an Abstract Obstacle Problem 10. Helmholtz Decomposition of Wp,S Vector Fields 11. Nonlinear Dispersive Waves and Variational Principles 12. A Priori Growth and Hslder Estimates for Harmonic Mappings 13. Conservation Laws in Gauge Field Theories 14. The Borel Spectral Sequence: Some Remarks and Applications 15. Newton, Euler, and Poe in the Calculus of Variations 16. Stability of Minimum Points for Problems with Constraints 17. Leonhard Euler: Mathematical Modeller and Model for Mathematicians 18. Noncommutative Calculus of Variations 19. On the Role of Reciprocity Conditions in the Formulation of Conservation Laws and Variational Principles 20. Variational Principles in Soliton Physics 21. Some Finite Codimensional Lie Subgroups of DiffW(M) 22. Exterior Forms and Optimal Control Theory 23. The Range of Relative Harmonic Dimensions 24. The Coincidence Set for Two-Dimensional Area Minimizing Surfaces in Rn Which Avoid a Convex Obstacle 25. On the Basins of Attraction of Gradient Vector Fields 26. Global Aspects of the Continuation Method 27. Applications of Smale Theory to the n-Body Problem of MechanIcs—Astronomy 28. On the Morse-Smale Index Theorem for Minimal Surfaces 29. A Cartan Form for the Field Theory of Carathodory in the Calculus of Variations of Multiple Integrals 30. The Ky Fan Minimax Principle, Sets with Convex Sections, and Variational Inequalities 31. Some Remarks about Variational Problems with Constraints Gerhard Strohmer 32. Inverse Problem: Its General Solution 33. On the Stability of a Functional Which is Approximately Additive or Approximately Quadratic on A-Orthogonal Vectors