عنوان

Variational Methods :

3662032120

9783662032121

b579284

Variational Methods :

[Book]

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

by Michael Struwe.

Second, rev. and Substantially Expanded edition

Berlin, Heidelberg

Springer Berlin Heidelberg

1996

(xvi, 272 pages)

Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, A Series of Modern Surveys in Mathematics, 34.

I. The Direct Methods in the Calculus of Variations --; II. Minimax Methods --; III. Limit Cases of the Palais-Smale Condition --; 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 Radò. 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.

Global analysis (Mathematics)

Mathematics.

Systems theory.

by Michael Struwe.

Michael Struwe

[Book]

Y