Extremal Arcs and Extended Hamiltonian Systems
Open Access
- 1 August 1977
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 231 (2) , 349-367
- https://doi.org/10.2307/1997908
Abstract
A general variational problem is considered; it involves the minimization of an integrand L of a very general nature. The Lagrangian L is allowed to assume the value , and need satisfy no differentiability or convexity conditions. A Hamiltonian corresponding to the problem is defined via the conjugate function of convex analysis, and it is shown how one obtains necessary conditions in the form of an extended Hamiltonian system. This system is expressed in terms of certain ``generalized gradients'' previously developed by the author.Keywords
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