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AuthorStruwe, Michael. author
TitleVariational Methods [electronic resource] : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems / by Michael Struwe
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996
Edition Second, Revised and Substantially Expanded Edition
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Descript XVI, 272 p. 8 illus. online resource


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 Radรฒ. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field


I. The Direct Methods in the Calculus of Variations -- II. Minimax Methods -- III. Limit Cases of the Palais-Smale Condition -- Appendix A -- Sobolev Spaces -- Hรถlder Spaces -- Imbedding Theorems -- Density Theorem -- Trace and Extension Theorems -- Poincarรฉ Inequality -- Appendix B -- Schauder Estimates -- Weak Solutions -- A Regularity Result -- Maximum Principle -- Weak Maximum Principle -- Application -- Appendix C -- Frรฉchet Differentiability -- Natural Growth Conditions -- References

Mathematics Mathematical analysis Analysis (Mathematics) System theory Calculus of variations Mathematics Systems Theory Control Calculus of Variations and Optimal Control; Optimization Analysis


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