Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

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.

Author Biography

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