Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

  • Authors
  • Wolfgang Reichel

Part of the Lecture Notes in Mathematics book series (LNM, volume 1841)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Wolfgang Reichel
    Pages 1-7
  3. Wolfgang Reichel
    Pages 9-26
  4. Wolfgang Reichel
    Pages 27-57
  5. Wolfgang Reichel
    Pages 89-125
  6. Wolfgang Reichel
    Pages 127-138
  7. Wolfgang Reichel
    Pages 139-143
  8. Wolfgang Reichel
    Pages 145-149
  9. Back Matter
    Pages 151-152

About this book

Introduction

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point?

A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

Keywords

Boundary value problem Calculus of Variations boundary value problems partial differential equation partial differential equations transformation groups uniqueness of critical points

Bibliographic information

  • DOI https://doi.org/10.1007/b96984
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21839-5
  • Online ISBN 978-3-540-40915-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book