An embedding theorem for weighted Sobolev classes on a John domain: case of weights that are functions of a distance to a certain h-set

Abstract

Let $\Omega$ be a John domain, and let $\Gamma\subset \partial \Omega$ be an $h$-set. For some functions $h$ and some weight functions depending on distance from $\Gamma$, embedding theorems for a weighted Sobolev class is obtained.