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Uniqueness theorems for variational problems by the method of transformation groups Wolfgang Reichel

Von:

Reichel, Wolfgang [aut]

Materialtyp: Text

TextVerlagsnummer: 10997833Sprache: Englisch Reihen: ; 184100 | Lecture notes in mathematics ; 1841Verlag: Berlin Heidelberg [u.a.] Springer 2004Beschreibung: XIII, 152 S graph. Darst 235 mm x 155 mmInhaltstyp:

Text

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ISBN:

3540218394

Schlagwörter: Andere physische Formen: Erscheint auch als: Uniqueness Theorems for Variational Problems by the Method of Transformation Groups; Online-Ausg.: Uniqueness Theorems for Variational Problems by the Method of Transformation GroupsLOC-Klassifikation:

Andere Klassifikation:

17,1
SI 850
SK 660
*35-02
35J20
35A30
47J30
49-02
49K20
49Q05
31.45
31.48

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Zusammenfassung: 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 andomegaeAndere Ausgaben: Erscheint auch als (Online-Ausgabe): / Reichel, Wolfgang: Uniqueness Theorems for Variational Problems by the Method of Transformation Groups; Online-Ausg.: / Reichel, Wolfgang: Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

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Titelinformationen ( 6 )

Exemplare
Medientyp	Aktuelle Bibliothek	Sammlung	Standort	Signatur	Status	Fälligkeitsdatum	Barcode
Buch	Gebäude E2 3 (UdS Campusbibliothek für Informatik und Mathematik)	Campusbibliothek für Informatik und Mathematik (E2 3)	Series (GF)	LNM 1841 (Regal durchstöbern(Öffnet sich unterhalb))	Verfügbar		2202000369776

Literaturverz. S. [145] - 149

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

Reichel, Wolfgang: Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

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