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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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