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