© 2004

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1841)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Wolfgang Reichel
    Pages 1-7
  3. Wolfgang Reichel
    Pages 9-26
  4. Wolfgang Reichel
    Pages 27-57
  5. Wolfgang Reichel
    Pages 89-125
  6. Wolfgang Reichel
    Pages 127-138
  7. Wolfgang Reichel
    Pages 139-143
  8. Wolfgang Reichel
    Pages 145-149
  9. Back Matter
    Pages 151-152

About this book


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.


Boundary value problem Calculus of Variations boundary value problems partial differential equation partial differential equations transformation groups uniqueness of critical points

About the authors

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 information

  • Book Title Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
  • Authors Wolfgang Reichel
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-21839-5
  • eBook ISBN 978-3-540-40915-1
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XIV, 158
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Calculus of Variations and Optimal Control; Optimization
    Partial Differential Equations
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