Uniqueness theorems for variational problems by the method of transformation groups

Author(s)

• Reichel, Wolfgang

Bibliographic Information

Uniqueness theorems for variational problems by the method of transformation groups

Wolfgang Reichel

（Lecture notes in mathematics, 1841）

Springer, c2004

Note

Includes bibliographical references (p. [145]-149) and index

Description and Table of Contents

Description

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.

Table of Contents

Introduction.- Uniqueness of Critical Points (I).- Uniqueness of Citical Pints (II).- Variational Problems on Riemannian Manifolds.- Scalar Problems in Euclidean Space.- Vector Problems in Euclidean Space.- Frechet-Differentiability.- Lipschitz-Properties of ge and omegae.

by "Nielsen BookData"

Details

• NCID: BA67370393
• ISBN:
  • 3540218394
• LCCN: 2004103794
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: xiii, 152 p.
• Size: 24 cm
• Parent Bibliography ID:
  • BA00146586