Embeddings and Widths of Weighted Sobolev Classes

Abstract

In this paper, embedding theorems for reduced weighted Sobolev classes \( \widehat{W}^r_{p,g}(\Omega) \) in Lebesgue spaces \( L_{q,v}(\Omega) \) are obtained. Here weight functions have singularity at the origin and \( v \notin L_q(\Omega) \). For some special weight functions order estimates for Kolmogorov, Gelfand and linear widths are obtained.