Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Author :
Publisher : Springer Science & Business Media
Total Pages : 172
Release :
ISBN-10 : 3540218394
ISBN-13 : 9783540218395
Rating : 4/5 (395 Downloads)

Book Synopsis Uniqueness Theorems for Variational Problems by the Method of Transformation Groups by : Wolfgang Reichel

Download or read book Uniqueness Theorems for Variational Problems by the Method of Transformation Groups written by Wolfgang Reichel and published by Springer Science & Business Media. This book was released on 2004-05-13 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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