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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

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Englisch
Springer Berlin Heidelbergerschienen am30.04.20042004
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.mehr
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Produkt

KlappentextA 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.
Details
Weitere ISBN/GTIN9783540409151
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2004
Erscheinungsdatum30.04.2004
Auflage2004
ReiheLecture Notes in Mathematics
Reihen-Nr.1841
SpracheEnglisch
IllustrationenXIV, 158 p.
Artikel-Nr.7458763
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

Autor

Studies: October 1987 -- January 1994 Diplom studies in mathematics at the University of KarlsruheOctober 1991 -- October 1992 Master of Science in nonlinear mathematics, University of Bath (U.K.)

Phd: January 1996 University of Karlsruhe

Habilitation: October 2001 University of Basel

Positions held: March 1994 -- June 1998 Scientific collaborator, Math. Institute, Univ. of KarlsruheOctober 1998 -- September 2002 Assistant, Math. Institute, University of BaselSommersemester 2000: Lecturer at the Univ. of ZurichWintersemester 2002/2003: Substitute professor at the Univ. of Giessen Since April 2003: Substitute professor at the Univ. of Basel

Stays at other institutions:October 1996 -- September 1998: postdoc at the Univ. of Minnesota (USA) and Univ. of Cologne with DFG-grantMarch,July, August 1999: visitor at the Univ. of Cardiff (U.K) with EPSRC-grant

Awards: April 1997: "Klaus-Tschira Price for comprehensible science" awarded for the doctoral thesis by the Univ. of Karlsruhe