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Widths of weighted Sobolev classes on a John domain: strong singularity at a point

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Abstract

The paper is concerned with orders of Kolmogorov and linear widths of weighted Sobolev classes on a domain with John condition in a weighted Lebesgue space. It is assumed that at zero the weights have singularity, which may have effect on the orders of weights.

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Notes

  1. Here \(r-d\) may be negative.

  2. Here \(C^\infty (\Omega )\) is the space of functions that are smooth on the open set \(\Omega \), but not necessarily extendable to smooth functions on the whole space \(\mathbb R ^d\).

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    A. A. Vasil’eva

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The research was carried out with the financial support of the Russian Foundation for Basic Research (grants no. 13-01-00022, 12-01-00554).

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Vasil’eva, A.A. Widths of weighted Sobolev classes on a John domain: strong singularity at a point. Rev Mat Complut 27, 167–212 (2014). https://doi.org/10.1007/s13163-013-0132-4

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