A Turnpike Result for a Class of Problems of the Calculus of Variations with Extended-Valued Integrands

We study the structure of approximate solutions of an autonomous variational problem with a lower semicontinuous integrand

where

R^n R n

is the

n n

-dimensional Euclidean space. We are interested in a turnpike property of the approximate solutions which are independent of the length of the interval, for all sufficiently large intervals.