Uniqueness theorems for variational problems by the method of transformation groups
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Bibliographic Information
Uniqueness theorems for variational problems by the method of transformation groups
(Lecture notes in mathematics, 1841)
Springer, c2004
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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.
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