Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
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"Uniqueness Theorems for Variational Problems by the Method of Transformation Groups" by Wolfgang Reichel is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
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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"Uniqueness Theorems for Variational Problems by the Method of Transformation Groups" by Wolfgang Reichel is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Core Mathematics
Author: Wolfgang Reichel
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
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.
| Author | Wolfgang Reichel |
| Publisher | Springer Science & Business Media |
| Published | 2004-05-13 |
| ISBN-13 | 9783540218395 |
| Binding | Paperback |
| Pages | 172 |
| Language | English |
| Subjects | Mathematics |
| Topic | Core Mathematics |
| Series | Lecture Notes in Mathematics |
Format: Paperback
Length: 172 pages
Language: English
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