Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und Ihrer ... /A Series of Modern Surveys in Mathematics) - hardcover

EAN (ISBN-13): 9783540664796
ISBN (ISBN-10): 3540664793
Hardcover
Paperback
Publishing year: 2000
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Book in our database since 2007-06-06T15:37:49+01:00 (London)
Detail page last modified on 2021-02-26T21:01:54+00:00 (London)
ISBN/EAN: 9783540664796

ISBN - alternate spelling:
3-540-66479-3, 978-3-540-66479-6
Alternate spelling and related search-keywords:
Book author: struwe, strwe, edition
Book title: ergebnisse, mathematik der, systems nonlinear partial differential equations, methods modern mathematics, grenzgebiete, surveys modern mathematics, variational methods

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Information from Publisher

Author: Michael Struwe
Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge; Variational Methods - A Series of Modern Surveys in Mathematics; Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Publisher: Springer; Springer Berlin
274 Pages
Publishing year: 1999-11-22
Berlin; Heidelberg; DE
Printed / Made in
Weight: 0,500 kg
Language: English
85,59 € (DE)
87,99 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Sonstiges; Kybernetik und Systemtheorie; Verstehen; manifold; calculus of variations; minimum; maximum; compactness; convergence; extrema; calculus; partial differential equation; Partial Differential Equations; banach spaces; Mathematical Physics; differential equation; hamiltonian system; Mathematica; C; Systems Theory, Control; Mathematics and Statistics; Calculus of Variations and Optimal Control; Optimization; Analysis; Variationsrechnung; Optimierung; Mathematische Analysis, allgemein; BB; BB; BC; EA

I. The Direct Methods in the Calculus of Variations.- 1. Lower Semi-Continuity.- Degenerate Elliptic Equations.- Minimal Partitioning Hypersurfaces.- Minimal Hypersurfaces in Riemannian Manifolds.- A General Lower Semi-Continuity Result.- 2. Constraints.- Semi-Linear Elliptic Boundary Value Problems.- Perron’s Method in a Variational Guise.- The Classical Plateau Problem.- 3. Compensated Compactness.- Applications in Elasticity.- Convergence Results for Nonlinear Elliptic Equations.- Hardy space methods.- 4. The Concentration-Compactness Principle.- Existence of Extremal Functions for Sobolev Embeddings.- 5. Ekeland’s Variational Principle.- Existence of Minimizers for Quasi-Convex Functionals.- 6. Duality.- Hamiltonian Systems.- Periodic Solutions of Nonlinear Wave-Equations.- 7. Minimization Problems Depending on Parameters.- Harmonic maps with singularities.- II. Minimax Methods.- 1. The Finite Dimensional Case.- 2. The Palais-Smale Condition.- 3. A General Deformation Lemma.- Pseudo-Gradient Flows on Banach Spaces.- Pseudo-Gradient Flows on Manifolds.- 4. The Minimax Principle.- Closed Geodesics on Spheres.- 5. Index Theory.- Krasnoselskii Genus.- Minimax Principles for Even Functionals.- Applications to Semilinear Elliptic Problems.- General Index Theories.- Ljusternik-Schnirelman Category.- A Geometrical S1-Index.- Multiple Periodic Orbits of Hamiltonian Systems.- 6. The Mountain Pass Lemma and its Variants.- Applications to Semilinear Elliptic Boundary Value Problems.- The Symmetric Mountain Pass Lemma.- Application to Semilinear Equations with Symmetry.- 7. Perturbation Theory.- Applications to Semilinear Elliptic Equations.- 8. Linking.- Applications to Semilinear Elliptic Equations.- Applications to Hamiltonian Systems.- 9. Parameter Dependence.- 10. Critical Points of Mountain Pass Type.- Multiple Solutions of Coercive Elliptic Problems.- 11. Non-Differentiable Functionals.- 12. Ljusternik-Schnirelman Theory on Convex Sets.- Applications to Semilinear Elliptic Boundary Value Problems.- III. Limit Cases of the Palais-Smale Condition.- 1. Pohožaev’s Non-Existence Result.- 2. The Brezis-Nirenberg Result.- Constrained Minimization.- The Unconstrained Case: Local Compactness.- Multiple Solutions.- 3. The Effect of Topology.- A Global Compactness Result.- Positive Solutions on Annular-Shaped Regions.- 4. The Yamabe Problem.- 5. The Dirichlet Problem for the Equation of Constant Mean Curvature.- Small Solutions.- The Volume Functional.- Wente’s Uniqueness Result.- Local Compactness.- Large Solutions.- 6. Harmonic Maps of Riemannian Surfaces.- The Euler-Lagrange Equations for Harmonic Maps.- Bochner identity.- The Homotopy Problem and its Functional Analytic Setting.- Existence and Non-Existence Results.- The Evolution of Harmonic Maps.- 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.
The 3rd edition gives a survey on recent developments in the field and the references have been updated.