Uniqueness Theorems for Variational Problems by the Method of Transformation Groups / by Wolfgang Reichel
(Lecture Notes in Mathematics ; 1841)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 2004 |
| 本文言語 | 英語 |
| 大きさ | XIV, 158 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Reichel, Wolfgang author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Partial differential equations LCSH:Calculus of variations FREE:Mathematics FREE:Calculus of Variations and Optimal Control; Optimization FREE:Partial Differential Equations |
| 分 類 | DC23:515.64 |
| 巻冊次 | ISBN:9783540409151 
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| ISBN | 9783540409151 |
| URL | http://dx.doi.org/10.1007/b96984 |
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