Uniqueness theorems for variational problems by the method of transformation groups
A classical problem in the calculus of variations is the investigation ofcritical 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. TOC: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 andomegae.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783540218395
3540218394
- Dimensions
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24 cm
- Extent
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XIII, 152 S.
- Language
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Englisch
- Notes
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graph. Darst.
Literaturverz. S. 145 - 149
- Bibliographic citation
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Lecture notes in mathematics ; Vol. 1841
- Classification
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Mathematik
- Keyword
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Variationsrechnung
Kritischer Punkt
Transformationsgruppe
Eindeutigkeitssatz
- Event
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Veröffentlichung
- (where)
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Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo
- (who)
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Springer
- (when)
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2004
- Creator
- Table of contents
- Rights
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Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Last update
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11.03.2025, 11:40 AM CET
Data provider
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Associated
- Reichel, Wolfgang
- Springer
Time of origin
- 2004
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