Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Author | : Wolfgang Reichel |
Publisher | : Springer |
Total Pages | : 158 |
Release | : 2014-03-12 |
ISBN-10 | : 3662175231 |
ISBN-13 | : 9783662175231 |
Rating | : 4/5 (231 Downloads) |
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.