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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. |
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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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Springer eBooks | 9783540409151 |
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EB00235928 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA402.5-402.6 LCC:QA315-316 DC23:519.6 DC23:515.64 |
書誌ID | 4000109064 |
ISBN | 9783540409151 |
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