Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

von Wolfgang Reichel

158 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783540218395
• Sprache: Englisch
• Erscheinungsdatum: 13.05.2004
• Genre: Mathematik/Sonstiges
• Verlag: Springer Berlin