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Structure of approximate solutions of variational problems with extended-valued convex integrands. (English) Zbl 1175.49002
Summary: We study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex 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 obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.

MSC:
49J15 Existence theories for optimal control problems involving ordinary differential equations
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