Variational Methods
Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
2nd Edition
Published on 10. September 1996
Book
Hardback
XVI, 272 pages
978-3-540-58859-7 (ISBN)
Description
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.
Reviews / Votes
From the reviews of the fourth edition:
"The fourth edition of Michael Struwe's book Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems was published in 2008, 18 years after the first edition. . The bibliography alone would make it a valuable reference as it contains nearly 500 references. . Struwe's book is addressed to researchers in differential geometry and partial differential equations." (John D. Cook, MAA Online, January, 2009)
More details
Series
Edition
2nd rev. and substantially expanded ed.
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Illustrations
8 s/w Abbildungen
16 figures
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
550 gr
ISBN-13
978-3-540-58859-7 (9783540588597)
DOI
10.1007/978-3-662-03212-1
Schweitzer Classification
Other editions
New editions
Michael Struwe
Variational Methods
Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Book
11/1999
3rd Edition
Springer
€85.59
Article exhausted; check for reprint
Previous edition
Michael Struwe
Variational Methods
Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Book
11/1990
Springer
€85.59
Article exhausted; check for reprint
Content
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.