On imbeddings of weighted Sobolev spaces

Abstract

We obtained the continuous (and also compact) imbedding $$W^1,p(ω, \nu₀,\nu₁)\mapsto W^1,p(ω, ω)$$ under certain conditions on weights, where $ω$ is a bounded domain in $R^N$. Also, for the case $\nu₀=\nu₁$, this imbedding is shown to exist under less restrictive conditions. Finally, the imbedding $$W^1,p(ω, \nu)\mapsto L^q(ω, ω),$$ already obtained by Gurka and Opic [3], is established under a different set of conditions.