A GENERIC TURNPIKE RESULT FOR A CLASS OF ONE-DIMENSIONAL VARIATIONAL PROBLEMS ARISING IN CONTINUUM MECHANICS

摘要

In this paper we study the structure of optimal solutions of one-dimensional second order variational problems arising in continuum mechanics. We are interested in a turnpike property of the optimal solutions which is independent of the length of the interval, for all sufficiently large intervals. To have this property means, roughly speaking, that the approximate solutions of the variational problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions. We establish that a generic integrand possess the turnpike property.