Geodesic
Estimates for the $n$-widths of compact sets of differentiate functions in spaces with weight functions
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 117-132

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We obtain two-sided estimates of the widths defined by A. N. Kolmogorov for the unit spheres of the anisotropic Sobolev-Slobodetskii spaces in $L_q(\mu)$ for an arbitrary measure, guaranteeing the compactness of the corresponding embedding. As shown by examples, these estimates turn out to be exact as far as the order is concerned for measures with a “strong” singularity and, in addition, they allow us to justify the formula of the classical spectral asymptotics under very weak (close to necessary) restrictions of the measure $\mu$. 
@article{ZNSL_1976_59_a5,
     author = {V. L. Oleinik},
     title = {Estimates for the $n$-widths of compact sets of differentiate functions in spaces with weight functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--132},
     publisher = {mathdoc},
     volume = {59},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a5/}
}
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V. L. Oleinik. Estimates for the $n$-widths of compact sets of differentiate functions in spaces with weight functions. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 117-132. http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a5/