Uniqueness Theorems for Variational Problems by the Method of Transformation Groups / / by Wolfgang Reichel

• Autore: Reichel Wolfgang
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004
• Edizione: 1st ed. 2004.
• Descrizione fisica: 1 online resource (XIV, 158 p.)
• Disciplina: 512
• Soggetto topico: Calculus of variations; Differential equations, Partial; Calculus of Variations and Optimal Control; Optimization; Partial Differential Equations
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [144]-149) and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Uniqueness theorems for variational problems by the method of transformation groups
• ISBN: 3-540-40915-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144618903321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1841