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  3. Uniqueness Theorems for Variational Problems by the Method of Transformation Groups (Repost)

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups (Repost)

Posted By: step778
Date: 4 Oct 2018 10:13:44
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups (Repost)

Wolfgang Reichel, "Uniqueness Theorems for Variational Problems by the Method of Transformation Groups"
2004 | pages: 135 | ISBN: 3540218394 | PDF | 1,5 mb

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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