Widths of weighted Sobolev classes on a domain with a peak: some limiting cases

TL;DR

This paper investigates the order estimates of various widths for weighted Sobolev classes on domains with peaks, focusing on specific weights in weighted Lebesgue spaces, to understand their limiting behaviors.

Contribution

It provides new order estimates for Kolmogorov, Gelfand, and linear widths of weighted Sobolev classes in peak domains under special weight conditions.

Findings

Derived order estimates for widths in peak domains.

Identified limiting cases for weighted Sobolev classes.

Enhanced understanding of the behavior of widths with specific weights.

Abstract

Order estimates for Kolmogorov, Gelfand and linear widths of a weighted Sobolev class on a domain with a peak in a weighted Lebesgue space are obtained for some special weights.