| Document Type
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BL
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| Record Number
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578606
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| Doc. No
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b407825
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| Main Entry
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Struwe, Michael.
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| Title & Author
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Variational Methods : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems /\ by Michael Struwe.
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| Edition Statement
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Third Edition.
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| Publication Statement
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Berlin, Heidelberg :: Springer Berlin Heidelberg :: Imprint: Springer,, 2000.
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| Series Statement
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Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics,; 34
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| ISBN
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9783662041949
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: 9783662041963
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| Contents
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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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| Abstract
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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 three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.
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| Subject
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Mathematics.
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Global analysis (Mathematics).
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| Subject
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Systems theory.
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| Subject
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Mathematical optimization.
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| Added Entry
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SpringerLink (Online service)
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