Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

By Wolfgang Reichel

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.

• Format: Paperback
• Language: English
• ISBN: 3540218394
• ISBN13: 9783540218395
• Release Date: May 2004
• Publisher: Springer
• Length: 158 Pages
• Weight: 0.91 lbs.
• Dimensions: 0.4" x 8.5" x 11.0"