Uniqueness theorems for variational problems by the method of transformation groups /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
[2004]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1841. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xiii, 152 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages [145]-149) and index. |
| ISBN: | 9783540409151 (electronic bk.) 3540409157 (electronic bk.) |
| ISSN: | 0075-8434 ; |