Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Taschenbuch

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Beschreibung

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spacesV. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying spaceVdoes {\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 groupGof transformations ofV, 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.

Haupt-Genre
Fachbücher
Sub-Genre
Mathematik & Naturwissenschaften
Format
Taschenbuch
Seitenzahl
158
Preis
34.95 €