s-Numbers of compact embeddings of function spaces on quasi-bounded domains

TL;DR

This paper derives asymptotic formulas for various s-numbers associated with Sobolev embeddings between Besov and Triebel-Lizorkin spaces on quasi-bounded domains, advancing understanding of their compactness properties.

Contribution

It provides new asymptotic estimates for approximation, Gelfand, Kolmogorov, and Weyl numbers of these embeddings on quasi-bounded domains, a topic not previously fully explored.

Findings

Asymptotic formulas for s-numbers of Sobolev embeddings

Enhanced understanding of compactness in function space embeddings

New results applicable to quasi-bounded domains

Abstract

We prove asymptotic formulas for the behavior of approximation, Gelfand, Kolmogorov and Weyl numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces defined on quasi-bounded domains.