The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Introducing the Dorfmanian: A Powerful Tool for the Calculus Of Variations


Olivier de La Grandville

Department of Management Science and Engineering,
Stanford University,
475 Via Ortega, Stanford, CA 94305,
U. S. A.



We show how a modified Hamiltonian proposed by Robert Dorfman [1] to give intuitive sense to the Pontryagin maximum principle can be extended to easily obtain all high-order equations of the calculus of variations. This new concept is particularly efficient to determine the differential equations leading to the extremals of functionals defined by n-uple integrals, while a traditional approach would require -- in some cases repeatedly -- an extension of Green's theorem to n-space.
Our paper is dedicated to the memory of Robert Dorfman (1916 - 2002).

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