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Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

REICHEL, WOLFGANG
SPRINGER
05 / 2004
9783540218395
978-35-4021-839-5
Inglês
Lecture Notes in Mathematics
Ingles
Optimizacion

Sinopse

A classical problem in the calculus of variations is the investigation ofnbsp;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.