Estimates for the Kolmogorov widths of weighted Sobolev classes with conditions on the $0$th and the greatest derivatives

TL;DR

This paper derives order estimates for the Kolmogorov widths of weighted Sobolev classes with specific boundary conditions, advancing understanding of approximation capabilities in weighted functional spaces.

Contribution

It provides new order estimates for Kolmogorov widths of weighted Sobolev classes with boundary conditions, filling a gap in approximation theory.

Findings

Order estimates for Kolmogorov widths are established.

Results apply to weighted Sobolev spaces with boundary conditions.

The estimates improve understanding of approximation limits in these spaces.

Abstract

In this article, we obtain the order estimates for the Kolmogorov widths of sets with conditions on the norm in the weighted Sobolev space $W^r_{p_1}$ and in the weighted space $L_{p_0}$.