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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Paperback
Series: Lecture Notes in Mathematics, Book 1841
General ComputersGeneral Mathematics
ISBN13: 9783540218395
Publisher: Springer Nature
Published: May 13 2004
Pages: 158
Weight: 0.91
Height: 0.37 Width: 8.50 Depth: 11.00
Language: English
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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