On imbeddings of weighted Sobolev spaces
Pankaj Kumar Jain · Università del Salento · 2009
We obtained the continuous (and also compact) imbedding $$W1,p(ω, u0, u1)\mapsto W1,p(ω, ω)$$ under certain conditions on weights, where $ω$ is a bounded domain in $RN$. Also, for the case $ u0= u1$, this imbedding is shown to exist under less restrictive conditions. Finally, the imbedding $$W1,p(ω, u)\mapsto Lq(ω, ω),$$ already obtained by Gurka and Opic [3], is established under a different set of conditions.