Author | Struwe, Michael. author |
---|---|
Title | Variational Methods [electronic resource] : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems / by Michael Struwe |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-04194-9 |
Descript | XVIII, 274 p. online resource |
I. The Direct Methods in the Calculus of Variations -- 1. Lower Semi-Continuity -- 2. Constraints -- 3. Compensated Compactness -- 4. The Concentration-Compactness Principle -- 5. Ekelandโs 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. Pohoลพaevโs 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 -- Hรถlder Spaces -- Imbedding Theorems -- Density Theorem -- Trace and Extension Theorems -- Poincarรฉ Inequality -- Appendix B -- Schauder Estimates -- Weak Solutions -- A Regularity Result -- Maximum Principle -- Weak Maximum Principle -- Application -- Appendix C -- Frรฉchet Differentiability -- Natural Growth Conditions -- References