Uniqueness Theorems for Variational Problems by the Method of Transformation Groups [electronic resource] / by Wolfgang Reichel.
Material type: TextSeries: Lecture Notes in Mathematics ; 1841Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004Description: XIV, 158 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540409151Subject(s): Mathematics | Differential equations, partial | Mathematical optimization | Mathematics | Calculus of Variations and Optimal Control; Optimization | Partial Differential EquationsAdditional physical formats: Printed edition:: No titleDDC classification: 515.64 LOC classification: QA315-316QA402.3QA402.5-QA402.6Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|
IMSc Library | IMSc Library | Link to resource | Available | EBK1233 |
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.
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.
There are no comments on this title.