Geodesic
Chattering on optimal trajectories of H\"older problems
Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 669-683

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2002_193_5_a2,
     author = {M. I. Zelikin},
     title = {Chattering  on optimal trajectories of {H\"older} problems},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {193},
     number = {5},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_5_a2/}
}
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M. I. Zelikin. Chattering  on optimal trajectories of H\"older problems. Sbornik. Mathematics, Tome 193 (2002) no. 5, pp. 669-683. http://geodesic.mathdoc.fr/item/SM_2002_193_5_a2/