A turnpike result for a class of problems of the calculus of variations with extended-valued integrands. (English) Zbl 1162.49017

Zaslavski, Alexander J.

J. Convex Anal. 15, No. 4, 869-890 (2008).

Summary: We study the structure of approximate solutions of an autonomous variational problem with a lower semicontinuous integrand \(f:\mathbb R^{n} \times\mathbb R^{n} \to\mathbb R^{1} \cup \{\infty\}\), where \(\mathbb R^n\) is the \(n\)-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.

MSC:

49J45

Methods involving semicontinuity and convergence; relaxation

Keywords:

good function; infinite horizon; overtaking optimal function; turnpike property