Kolmogorov widths of the class $W_1^1$.

We will consider a classical problem of approximation – finding orders of decay for Kolmogorov widths of Sobolev classes on a segment, $d_n(W^r_p,L_q)$. These widths were actively studied by a number of mathematicians in 1960s and 1970s and sharp order estimates were obtained for all integer $r$ and all $p$,$q$, except the case $W_1^1$. Upper and lower bounds for this class contained a logarithmic gap which was only recently removed: https://arxiv.org/abs/2502.06716