Embeddings of Sobolev Spaces with Weights of Power Type

Abstract

The paper deals with some properties of the weighted Sobolev spaces $W_0^{k,p},W_M^{k,p}$ and $H^{k,p}$, with weights which are powers of the distance from a part $M$ of the boundary of the domain of definition. Conditions are given which guarantee the mutual ernbeddings of these spaces and the equivalence of certain norms. The paper generalizes some results of [1] and verifies a conjecture formulated in [2].

A correction to this paper is available.