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

Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

Authors: Struwe, Michael

  • The 4th edition now includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up
  • Smaller changes throughout the text have been made and references have been updated
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About this book

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 fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Also the recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. Aside from these more significant additions, a number of smaller changes throughout the text have been made and the references have been updated.

About the authors

Michael Struwe is full Professor of Mathematics at ETH Zurich.

Prof. Struwe was born on October 6, 1955 in Wuppertal, Germany. He studied mathematics at the University of Bonn. After receiving his doctorate in 1980, he was a member of the scientific staff in the special research sector 72 of the German research foundation and later an assistant at the Mathematical Institute of the University of Bonn. He spent extended research visits in Paris and at the ETH Zurich. In 1984 he was awarded the Felix Hausdorff Prize of the University of Bonn.

On April 1, 1986 Michael Struwe was appointed assistant professor, on October 1, 1990 associate professor and in 1993 he became full Professor of Mathematics at the ETH Zurich. From October, 2002 to September, 2004 he served as head of the ETH Mathematics Department. His research focuses on non-linear partial differential equations and the calculus of variations as well as their applications in mathematical physics and differential geometry.

In 2006 he received the Credit Suisse Award For Best Teaching.

He is editor of the series «Lectures in Mathematics, ETH Zürich» and co-editor of the series «Zurich Lectures in Advanced Mathematics»; moreover, he is co-editor of the journals «Calculus of Variations», «Duke Mathematical Journal», and «International Mathematical Research Notices».

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)

“This is the fourth edition of a standard reference work on direct methods in the calculus of variations. … The book contains a wealth of important results that would otherwise be hard to find in one single place.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 160 (4), July, 2010)


Table of contents (3 chapters)

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-540-74013-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-540-74012-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-642-09329-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Methods
Book Subtitle
Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
34
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-74013-1
DOI
10.1007/978-3-540-74013-1
Hardcover ISBN
978-3-540-74012-4
Softcover ISBN
978-3-642-09329-6
Series ISSN
0071-1136
Edition Number
4
Number of Pages
XX, 302
Topics