Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Wolfgang Reichel

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Editorial:
Springer Nature B.V.
Año de edición:
2014
ISBN:
9783662175231
48,40 €
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Sobre IBD

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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