Uniqueness Theorems for Variational Problems by the Method of Transformation Groups / by Wolfgang Reichel.

Format:

Book

Author/Creator:

Reichel, Wolfgang, 1968- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1841.

Lecture Notes in Mathematics, 0075-8434 ; 1841

Language:

English

Subjects (All):

Mathematical optimization.

Differential equations, Partial.

Calculus of Variations and Optimal Control; Optimization.

Partial Differential Equations.

Local Subjects:

Calculus of Variations and Optimal Control; Optimization.

Partial Differential Equations.

Physical Description:

1 online resource (XIV, 158 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540409151

Access Restriction:

Restricted for use by site license.