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Variational Methods : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems /

By: Struwe, Michael [author.].
Contributor(s): SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics: 344Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: XX, 302 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540740131.Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | System theory | Calculus of variations.1 | Mathematics.2 | Systems Theory, Control.2 | Calculus of Variations and Optimal Control; Optimization.2 | Analysis.2DDC classification: 519 Online resources: Click here to access online
Contents:
The Direct Methods in the Calculus of Variations -- Lower Semi-Continuity -- Constraints -- Compensated Compactness -- The Concentration-Compactness Principle -- Ekeland's Variational Principle -- Duality -- Minimization Problems Depending on Parameters -- Minimax Methods -- The Finite Dimensional Case -- The Palais-Smale Condition -- A General Deformation Lemma -- The Minimax Principle -- Index Theory -- The Mountain Pass Lemma and its Variants -- Perturbation Theory -- Linking -- Parameter Dependence -- Critical Points of Mountain Pass Type -- Non-Differentiable Functionals -- Ljusternik-Schnirelman Theory on Convex Sets -- Limit Cases of the Palais-Smale Condition -- Pohozaev's Non-Existence Result -- The Brezis-Nierenberg Result -- The Effect of Topology -- The Yamabe Problem -- The Dirichlet Problem for the Equation of Constant Mean Curvature -- Harmonic Maps of Riemannian Surfaces -- Appendix A -- Appendix B -- Appendix C -- References -- Index.
In: Springer eBooks0Summary: 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 Rad�. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK10390
Total holds: 0

The Direct Methods in the Calculus of Variations -- Lower Semi-Continuity -- Constraints -- Compensated Compactness -- The Concentration-Compactness Principle -- Ekeland's Variational Principle -- Duality -- Minimization Problems Depending on Parameters -- Minimax Methods -- The Finite Dimensional Case -- The Palais-Smale Condition -- A General Deformation Lemma -- The Minimax Principle -- Index Theory -- The Mountain Pass Lemma and its Variants -- Perturbation Theory -- Linking -- Parameter Dependence -- Critical Points of Mountain Pass Type -- Non-Differentiable Functionals -- Ljusternik-Schnirelman Theory on Convex Sets -- Limit Cases of the Palais-Smale Condition -- Pohozaev's Non-Existence Result -- The Brezis-Nierenberg Result -- The Effect of Topology -- The Yamabe Problem -- The Dirichlet Problem for the Equation of Constant Mean Curvature -- Harmonic Maps of Riemannian Surfaces -- Appendix A -- Appendix B -- Appendix C -- References -- Index.

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 Rad�. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.

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