Lecture Notes in Mathematics

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Authors: Reichel, Wolfgang

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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.

About the authors

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

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-540-40915-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-21839-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1841
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-40915-1
DOI
10.1007/b96984
Softcover ISBN
978-3-540-21839-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 158
Topics