Embeddings and widths of weighted Sobolev classes

In this paper, embedding theorems for reduced weighted Sobolev classes $\hat{W}_{p,g}^r(\Omega)$ 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.