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© 1996

Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge book series (MATHE3, volume 34)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Michael Struwe
    Pages 74-168
  3. Michael Struwe
    Pages 169-236
  4. Back Matter
    Pages 237-272

About this book

Introduction

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.

Keywords

Hamiltonian Systems Mathematica Mathematical Physics Partial Differential Equations calculus calculus of variations differential equation hamiltonian system maximum minimum partial differential equation

Authors and affiliations

  1. 1.Mathematik, ETH-ZentrumETH ZürichZürichSwitzerland

Bibliographic information

  • Book Title Variational Methods
  • Book Subtitle Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
  • Authors Michael Struwe
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
  • DOI https://doi.org/10.1007/978-3-662-03212-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-58859-7
  • Softcover ISBN 978-3-662-03214-5
  • eBook ISBN 978-3-662-03212-1
  • Series ISSN 0071-1136
  • Edition Number 2
  • Number of Pages XVI, 272
  • Number of Illustrations 8 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as a monograph
  • Topics Systems Theory, Control
    Calculus of Variations and Optimal Control; Optimization
    Analysis
  • Buy this book on publisher's site
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Reviews

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)