Adjoint problems in the multiple integral calculus of variations

Abstract :

A discussion of Haar’s work in which adjoint problems had their origin. Haar is followed in that a variational problem involving a special non-parameter-invariant lagrangian with its extremals is considered and an adjoint variational problem with its extremals is constructed by means of a parameter-invariant function. Discusses the theory of two-dimensional minimal surfaces and their bearing on adjoint variational problems. Various transformations are considered. One of these, which was developed by Caratheodory for the purpose of his last and most famous canonical formalism, is found to yield a partial generalization of the results obtained. Devoted to a full generalization of Haar’s theory involving lagrangians that are more general than those considered in the preceding chapters. The theory presented is due to Rund, who transformed carathedory’s canonical formalism into a fresh geometrical formalism. Within the framework of Rund’s theory adjoint problems are approached with a consideration of extensive and analytically significant conditions for integrability rather than an initial assumption of integrability. The theory is applied to the lagrangian associated with plateau’s problem and a result of a problematic nature is obtained.

 

Details

Author Myburgh WT
URL http://hdl.handle.net/20.500.11892/136562
Date Accessioned 2016-09-22T11:50:30Z
Date Available 2016-09-22T11:50:30Z
Date Created 1977
Identifier URL 1979
Language English
Subject Mathematics, Mathematical statistics and Statistics
Subject 2 Mathematics, Mathematical statistics and Statistics
Alternative Title
Degree Type Masters degree
Degree Description  MA