Widths and entropy numbers of embeddings of Sobolev classes on a H\"{o}lder domain

TL;DR

This paper improves upper bounds for entropy numbers and other widths of Sobolev classes on Hölder domains, providing sharper estimates for their compactness and approximation properties.

Contribution

It advances the understanding of Sobolev embeddings by refining upper estimates for entropy numbers and related widths on Hölder domains, extending previous results.

Findings

Improved upper estimates for entropy numbers of Sobolev classes

Derived upper bounds for Kolmogorov, linear, and Gelfand widths

Enhanced understanding of the compactness properties of Sobolev embeddings

Abstract

In the present paper we improve Besov's recent result about upper estimates for the entropy numbers of Sobolev classes on a H\"{o}lder domain (in the case when the definition of the Sobolev class involves all partial derivatives of order $r$). We also obtain upper estimates for the Kolmogorov, linear and the Gelfand widths.