Effective content of the calculus of variations I: Semi-continuity and the chattering lemma

Annals of Pure and Applied Logic 78 (1-3):127-146 (1996)

The content of existence theorems in the calculus of variations has been explored and an effective treatment of semi-continuity has been achieved. An algorithm has been developed which captures the natural algorithmic content of the notion of a semi-continuous function and this is used to obtain an effective version of the “chattering lemma” of control theory and ordinary differential equations. This lemma reveals the main computational content of the theory of relaxed optimal control
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DOI 10.1016/0168-0072(95)00034-8
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References found in this work BETA

Nicht Konstruktiv Beweisbare Sätze der Analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Computable Functionals.A. Grzegorczyk - 1959 - Journal of Symbolic Logic 24 (1):50-51.
Computable Analysis.S. Mazur, A. Grzegorczyk & H. Rasiowa - 1971 - Journal of Symbolic Logic 36 (1):148-150.
Recursive Metric Spaces.Y. N. Moschovakis - 1966 - Journal of Symbolic Logic 31 (4):651-652.

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Lp‐Computability.Ning Zhong & Bing-Yu Zhang - 1999 - Mathematical Logic Quarterly 45 (4):449-456.

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