Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Reichel, Wolfgang

ISBN 10: 3540218394 / ISBN 13: 9783540218395

Edité par Springer 2004-05, 2004

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N° de réf. du vendeur 6666-IUK-9783540218395

Détails bibliographiques

• Titre: Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
• Éditeur: Springer 2004-05
• Date de parution: 2004
• Langue: anglais
• ISBN à 10 chiffres: 3540218394
• ISBN à 13 chiffres: 9783540218395
• Reliure: PF
• État de l'article: New

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Synopsis

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.

À propos de l?auteur

Studies:
October 1987 -- January 1994 Diplom studies in mathematics at the University of Karlsruhe
October 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 Karlsruhe
October 1998 -- September 2002 Assistant, Math. Institute, University of Basel
Sommersemester 2000: Lecturer at the Univ. of Zurich
Wintersemester 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-grant
March, 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