{"product_id":"uniqueness-theorems-for-variational-problems-by-the-method-of-transformation-groups-2004","title":"Uniqueness Theorems for Variational Problems by the Method of Transformation Groups","description":"\u003cp\u003e\"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.\u003c\/p\u003e\n\u003cp\u003eA 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.\u003c\/p\u003e","brand":"Springer Science \u0026 Business Media","offers":[{"title":"Default Title","offer_id":46417015668935,"sku":"1-99-510-003207","price":49.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0736\/9575\/6487\/files\/9783540218395.jpg?v=1776285023","url":"https:\/\/snowflakeskies.com\/products\/uniqueness-theorems-for-variational-problems-by-the-method-of-transformation-groups-2004","provider":"Snowflake Skies","version":"1.0","type":"link"}