Geodesic
Chattering on optimal trajectories of Hölder problems
Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 669-683 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Chattering on optimal trajectories of {H\"older} problems},
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     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_5_a2/}
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M. I. Zelikin. Chattering on optimal trajectories of Hölder problems. Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 669-683. http://geodesic.mathdoc.fr/item/SM_2002_193_5_a2/

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