Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

• Main Author: Reichel, Wolfgang (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1841
• Subjects: Calculus of variations.; Partial differential equations.; Calculus of Variations and Optimal Control; Optimization.; Partial Differential Equations.

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...

Table of Contents:

• Introduction
• Uniqueness of Critical Points (I)
• Uniqueness of Citical Pints (II)
• Variational Problems on Riemannian Manifolds
• Scalar Problems in Euclidean Space
• Vector Problems in Euclidean Space
• Fréchet-Differentiability
• Lipschitz-Properties of ge and omegae.