Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Wolfgang Reichel, Reichel

ISBN 10: 3662175231 / ISBN 13: 9783662175231

Editore: Springer Nature B.V., 2014

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Titolo: Uniqueness Theorems for Variational Problems...

Casa editrice: Springer Nature B.V.

Data di pubblicazione: 2014

Legatura: PAP

Condizione: New

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Riassunto:

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.