Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

1. Auflage 2004
ISBN: 978-3-540-21839-5
Verlag: Springer

Buch, Englisch, Band 1841, 158 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 550 g

Reihe: Lecture Notes in Mathematics

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces . The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space 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 of transformations of , 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.

Zielgruppe

Research

Autoren/Hrsg.

Reichel, Wolfgang

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Operations Research Spieltheorie

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.

Über Autor(innen)

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