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＜電子ブック＞
Variational Methods : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems / by Michael Struwe
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 34)

版	3rd ed. 2000.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	XVIII, 274 p : online resource
冊子体	Variational methods : applications to nonlinear partial differential equations and Hamiltonian systems / Michael Struwe
著者標目	*Struwe, Michael author SpringerLink (Online service)
件　名	LCSH:System theory LCSH:Control theory LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Mathematical analysis FREE:Systems Theory, Control FREE:Calculus of Variations and Optimization FREE:Analysis
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-04194-9

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