Abstract:
Estimates for the Kolmogorov widths in the Lq,v-metric of weighted Sobolev classes as well as for the approximation numbers of the corresponding embedding operators are found.
Bibliography: 33 titles.
\Bibitem{Vas10}
\by A.~A.~Vasil'eva
\paper Estimates for the widths of weighted Sobolev classes
\jour Sb. Math.
\yr 2010
\vol 201
\issue 7
\pages 947--984
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Linking options:
https://www.mathnet.ru/eng/sm7520
https://doi.org/10.1070/SM2010v201n07ABEH004098
https://www.mathnet.ru/eng/sm/v201/i7/p15
This publication is cited in the following 10 articles:
A. A. Vasileva, “Kolmogorovskie poperechniki peresecheniya dvukh vesovykh klassov Coboleva na otrezke s odinakovoi gladkostyu”, Tr. IMM UrO RAN, 29, no. 4, 2023, 55–63
I. V. Boikov, V. A. Ryazantsev, “On the optimal approximation of geophysical fields”, Num. Anal. Appl., 14:1 (2021), 13–29
Vasil'eva A.A., “Widths of Weighted Sobolev Classes With Constraints F(a) = Center Dot Center Dot Center Dot = F(K-1)(a) = F(K)(B) = Center Dot Center Dot Center Dot = F(R-1)(B)=0 and the Spectra of Nonlinear Differential Equations”, Russ. J. Math. Phys., 24:3 (2017), 376–398
E. N. Lomakina, “On estimates of the approximation numbers of the Hardy operator”, Eurasian Math. J., 6:2 (2015), 41–62
Gasiorowska A. Skrzypczak L., “Some S-Numbers of Embeddings of Function Spaces with Weights of Logarithmic Type”, Math. Nachr., 286:7, SI (2013), 644–658
A. Gogatishvili, V. D. Stepanov, “Reduction theorems for weighted integral inequalities on the cone of monotone functions”, Russian Math. Surveys, 68:4 (2013), 597–664
A. A. Vasilyeva, “Kolmogorov widths and approximation numbers of Sobolev classes with singular weights”, St. Petersburg Math. J., 24:1 (2013), 1–27
Zhang Sh., Fang G., “Gelfand and Kolmogorov Numbers of Sobolev Embeddings of Weighted Function Spaces”, J. Complex., 28:2 (2012), 209–223
Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights. II”, Russ. J. Math. Phys., 18:4 (2011), 465–504
Vasil'eva A.A., “Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights”, Russ. J. Math. Phys., 18:3 (2011), 353–385
Citation in format AMSBIB
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