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Variational Methods Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of th...

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Bibliographic Details
Main Author: Struwe, Michael
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2000, 2000
Edition:3rd ed. 2000
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Subjects:
Mathematical Analysis
Calculus Of Variations And Optimization
Control Theory
Systems Theory, Control
Analysis
System Theory
Mathematical Optimization
Calculus Of Variations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. The Direct Methods in the Calculus of Variations
  • 1. Lower Semi-Continuity
  • 2. Constraints
  • 3. Compensated Compactness
  • 4. The Concentration-Compactness Principle
  • 5. Ekeland’s Variational Principle
  • 6. Duality
  • 7. Minimization Problems Depending on Parameters
  • II. Minimax Methods
  • 1. The Finite Dimensional Case
  • 2. The Palais-Smale Condition
  • 3. A General Deformation Lemma
  • 4. The Minimax Principle
  • 5. Index Theory
  • 6. The Mountain Pass Lemma and its Variants
  • 7. Perturbation Theory
  • 8. Linking
  • 9. Parameter Dependence
  • 10. Critical Points of Mountain Pass Type
  • 11. Non-Differentiable Functionals
  • 12. Ljusternik-Schnirelman Theory on Convex Sets
  • III. Limit Cases of the Palais-Smale Condition
  • 1. Pohožaev’s Non-Existence Result
  • 2. The Brezis-Nirenberg Result
  • 3. The Effect of Topology
  • 4. The Yamabe Problem
  • 5. The Dirichlet Problem for the Equation of Constant Mean Curvature
  • 6. Harmonic Maps of Riemannian Surfaces
  • Appendix A
  • Sobolev Spaces
  • Hölder Spaces
  • Imbedding Theorems
  • Density Theorem
  • Trace and Extension Theorems
  • Poincaré Inequality
  • Appendix B
  • Schauder Estimates
  • Weak Solutions
  • A Regularity Result
  • Maximum Principle
  • Weak Maximum Principle
  • Application
  • Appendix C
  • Fréchet Differentiability
  • Natural Growth Conditions
  • References

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