Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Springer Berlin (Verlag)
978-3-540-21839-5 (ISBN)
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.
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
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.
| Erscheint lt. Verlag | 13.5.2004 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XIV, 158 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 265 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | Boundary value problem • boundary value problems • Calculus of Variations • partial differential equation • Partial differential equations • transformation groups • Transformation (Math.) • Transformation (Mathematik) • uniqueness of critical points |
| ISBN-10 | 3-540-21839-4 / 3540218394 |
| ISBN-13 | 978-3-540-21839-5 / 9783540218395 |
| Zustand | Neuware |
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