ADJOINT PROBLEMS IN THE CALCULUS OF VARIATIONS OF MULTIPLE INTEGRALS
作者:
Hanno Rund,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1976)
卷期:
Volume 1,
issue 1
页码: 29-82
ISSN:1607-3606
年代: 1976
DOI:10.1080/16073606.1976.9632514
出版商: Taylor & Francis Group
关键词: 49C10;49F10;35A30
数据来源: Taylor
摘要:
A general theory of adjoint variational problems is formulated for essentially arbitrary Lagrangians involving m independent and n dependent variables, together with the first derivatives of the latter, This approach contains as a special case the theory of Haar [4], in which the Lagrangian may depend solely on the derivatives of a single dependent function of two arguments. Because of the eventual occurrence of possibly incompatible sets of integrability conditions, the basic theory is developed against the background of non-integrable m-dimensional subspaces, which is in sharp contrast to the traditional approach to the calculus of variations. Relatively self-adjoint Lagrangians are defined and completely characterized in terms of an arbitrary Riemannian metric. In the course of the general theory certain geometric object fields are encountered in a very natural manner, some of which had arisen previously in the canonical formalism proposed by Caratheodory [2]. Accordingly the analysis of the present paper may serve to shed some light on this conceptually extremely difficult formalism.
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