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Record Nr. |
UNINA9910144618903321 |
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Autore |
Reichel Wolfgang |
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Titolo |
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups / / by Wolfgang Reichel |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004 |
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ISBN |
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Edizione |
[1st ed. 2004.] |
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Descrizione fisica |
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1 online resource (XIV, 158 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1841 |
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Disciplina |
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Soggetti |
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Calculus of variations |
Differential equations, Partial |
Calculus of Variations and Optimal Control; Optimization |
Partial Differential Equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages [144]-149) and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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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