Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Reichel, Wolfgang.
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups [electronic resource] / by Wolfgang Reichel. - XIV, 158 p. online resource. - Lecture Notes in Mathematics, 1841 0075-8434 ; . - Lecture Notes in Mathematics, 1841 .
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 on normed spaces V. The present work addresses the question: Under what conditions on the functional and the underlying space V does 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 . 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.
9783540409151
10.1007/b96984 doi
Mathematical optimization.
Differential equations, partial.
Calculus of Variations and Optimal Control; Optimization.
Partial Differential Equations.
QA315-316 QA402.3 QA402.5-QA402.6
515.64
Uniqueness Theorems for Variational Problems by the Method of Transformation Groups [electronic resource] / by Wolfgang Reichel. - XIV, 158 p. online resource. - Lecture Notes in Mathematics, 1841 0075-8434 ; . - Lecture Notes in Mathematics, 1841 .
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 on normed spaces V. The present work addresses the question: Under what conditions on the functional and the underlying space V does 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 . 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.
9783540409151
10.1007/b96984 doi
Mathematical optimization.
Differential equations, partial.
Calculus of Variations and Optimal Control; Optimization.
Partial Differential Equations.
QA315-316 QA402.3 QA402.5-QA402.6
515.64