Geodesic
On Sharp Constants in Inequalities for the Modulus of a~Derivative
Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 104-126.

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For every $1\le r\le\infty$, we solve a Kolmogorov-type problem of describing all triples of numbers $\mu _0,\mu _1,\mu _2\ge 0$ for which there exists a function $f$ with an absolutely continuous derivative on the interval $[0,1]$ such that $\|f\|_{L_\infty (0,1)}=\mu _0$, $|f'(x)|=\mu _1$, and $\|f''\|_{L_r(0,1)}=\mu _2$, where $x$ is a fixed point in the interval $[0,1]$. 
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V. I. Burenkov; V. A. Gusakov. On Sharp Constants in Inequalities for the Modulus of a~Derivative. Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 104-126. http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a9/

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