Geodesic
Approximation of Sobolev Classes by Their Finite-Dimensional Sections
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 370-382.

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We consider relative widths characterizing the best approximation of a fixed set by its sections of given dimension. For Sobolev classes of periodic functions of a single variable with constraints in $L_\infty$ or $L_1$ on higher-order derivatives, we present the exact orders of such widths in the spaces $L_q$. 
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V. N. Konovalov. Approximation of Sobolev Classes by Their Finite-Dimensional Sections. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 370-382. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a5/

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