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AuthorReichel, Wolfgang. author
TitleUniqueness Theorems for Variational Problems by the Method of Transformation Groups [electronic resource] / by Wolfgang Reichel
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2004
Connect tohttp://dx.doi.org/10.1007/b96984
Descript XIV, 158 p. online resource

SUMMARY

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


CONTENT

Introduction -- Uniqueness of Critical Points (I) -- Uniqueness of Citical Pints (II) -- Variational Problems on Riemannian Manifolds -- Scalar Problems in Euclidean Space -- Vector Problems in Euclidean Space -- Frรฉchet-Differentiability -- Lipschitz-Properties of ge and omegae


Mathematics Partial differential equations Calculus of variations Mathematics Calculus of Variations and Optimal Control; Optimization Partial Differential Equations



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