Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Reichel, Wolfgang

ISBN 10: 3662175231 / ISBN 13: 9783662175231

Edité par Springer, 2014

In. N° de réf. du vendeur ria9783662175231_new

Synopsis :

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.

Détails bibliographiques

Titre : Uniqueness Theorems for Variational Problems...
Éditeur : Springer
Date d'édition : 2014
Reliure : Couverture souple
Etat : New