Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Reichel, Wolfgang

ISBN 10: 3540218394 / ISBN 13: 9783540218395

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2004

A classical problem in the calculus of variations is the investigation of critical points of functionals {cal L on normed spaces V. This 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. Series: Lecture Notes in Mathematics. Num Pages: 158 pages, biography. BIC Classification: PBKQ. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 9. Weight in Grams: 550. . 2004. Paperback. . . . . Seller Inventory # V9783540218395

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.

About the Author:

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

Bibliographic Details

Title: Uniqueness Theorems for Variational Problems...
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Publication Date: 2004
Binding: Soft cover
Condition: New