Some remarks on a class of weight functions

Abstract

summary:In this paper we obtain some results about a class of functions $\rho\,:\, \Omega\rightarrow R_+$, where $\Omega$ is an open set of $R^n$, which are related to the distance function from a fixed subset $S_\rho\subset\partial\Omega$. We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function $\rho$.