Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
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Beschreibung
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.
Includes supplementary material: sn.pub/extras
Autor*in
Wolfgang Reichel
Themen in »Uniqueness Theorems for Variational Problems by the Method of Transformation Groups«
Boundary value problem Calculus of Variations boundary value problems partial differential equation partial differential equations transformation groups uniqueness of critical points