Lecture Notes in Mathematics

Reichel, Wolfgang

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.

Details

Published by: Springer

Publication Date: 2004-05-13

Format: Paperback

ISBN-13: 9783540218395

DOI: 10.1007/b96984

Dimensions: 235cm x155cm

Pages: 158