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Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups
- Collana:
- Lecture Notes In Mathematics
- EAN:
9783540218395
- ISBN:
3540218394
- Pagine:
- 158
- Formato:
- Paperback
- Lingua:
- Tedesco
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Descrizione Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups
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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