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＜電子ブック＞
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups / by Wolfgang Reichel
(Lecture Notes in Mathematics. ISSN:16179692 ; 1841)

版	1st ed. 2004.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	XIV, 158 p : online resource
著者標目	*Reichel, Wolfgang author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations FREE:Calculus of Variations and Optimization FREE:Differential Equations
一般注記	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 HTTP:URL=https://doi.org/10.1007/b96984

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