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

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Résumé :
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.

Biographie:
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

Sommaire:
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.- Fr?chet-Differentiability.- Lipschitz-Properties of ge and omegae.