Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

  • Michael Struwe

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Pages 74-168
  3. Back Matter
    Pages 263-302

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.


Calculus of Variations Hamiltonian Systems Mathematical Physics Partial Differential Equations Plateau's problem calculus compactness differential equation minimum partial differential equation

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  • Michael Struwe

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