Uniqueness Theorems for Variational Problems by the Method of Transformation Groups [electronic resource] / by Wolfgang Reichel.
Material type: TextSeries: Lecture Notes in Mathematics ; 1841Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004Description: XIV, 158 p. online resourceContent type:- text
- computer
- online resource
- 9783540409151
- 515.64 23
- QA315-316
- QA402.3
- QA402.5-QA402.6
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 -- Fréchet-Differentiability -- Lipschitz-Properties of ge and omegae.
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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