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
Total Pages : 158
Release :
ISBN-10 : 3662175231
ISBN-13 : 9783662175231
Rating : 4/5 (231 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. This book was released on 2014-03-12 with total page 158 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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