TY  - BOOK
AU  - Reichel,Wolfgang
ED  - SpringerLink (Online service)
TI  - Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
T2  - Lecture Notes in Mathematics,
SN  - 9783540409151
AV  - QA315-316 
U1  - 515.64 23
PY  - 2004///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differential equations, partial
KW  - Mathematical optimization
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Partial Differential Equations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b96984
ER  -