عنوان

Variational Methods

(Number (ISBN

9783662041949

(Number (ISBN

9783662041963

Number

b407825

Title Proper

Variational Methods

General Material Designation

[Book]

Other Title Information

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems /

First Statement of Responsibility

by Michael Struwe.

Edition Statement

Third Edition.

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

2000.

Series Title

Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics,

Volume Designation

34

ISSN of Series

0071-1136 ;

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9783662041963

Title

Springer eBooks

Global analysis (Mathematics).

Mathematical optimization.

Mathematics.

Systems theory.

Struwe, Michael.

SpringerLink (Online service)

Date of Transaction

20190307163000.0

Electronic name

[Book]

Y