Uniqueness theorems for variational problems by the method of transformation groups
By: Wolfgang Reichel.
Series: Lecture notes in mathematics,; 1841; Lecture notes in mathematics (Springer-Verlag) ;; 1841.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 152
Subjects: Transformation groups; Calculus of variations; Transformations (Mathematics)
Description: 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.
Notes: Includes bibliographical references (p. [144]-149) and index.