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Chattering on optimal trajectories of Hölder problems
M. I. Zelikin M. V. Lomonosov Moscow State University
Abstract:
The problem of the minimization of the mean-square deviation from the origin is studied in the class of functions on a half-axis with derivatives satisfying the Hölder condition. The support of the solution is shown to be a finite interval and the optimal function makes countably many switches from intervals of maximum increase of the velocity to intervals of
its maximum decrease. Switches accumulate to the right end-point of the support. An application of the results to the problem of precise constants in Kolmogorov-type inequalities for fractional derivatives is presented.
Received: 19.06.2001
Citation:
M. I. Zelikin, “Chattering on optimal trajectories of Hölder problems”, Mat. Sb., 193:5 (2002), 37–52; Sb. Math., 193:5 (2002), 669–683
Linking options:
https://www.mathnet.ru/eng/sm650https://doi.org/10.1070/SM2002v193n05ABEH000650 https://www.mathnet.ru/eng/sm/v193/i5/p37
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Abstract page: | 509 | Russian version PDF: | 205 | English version PDF: | 8 | References: | 95 | First page: | 3 |
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