Geodesic
Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the~space $L_p(\Omega;\omega)$
Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 275-290

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Several conditions on the weight functions $v$ and $\omega$ are obtained that guarantee the embedding inequality $$ \|u\|_{L_p(\Omega;\omega)}\leqslant C\biggl[\biggl(\int_\Omega|\nabla_lu|^p\biggr)^{1/p}+\biggl(\int_\Omega|u|^pv\biggr)^{1/p}\biggr], \qquad 1

/l. $$ Classes of weights $\omega$ and $v$ in which these conditions are both necessary and sufficient are described. 
@article{SM_2000_191_2_a4,
     author = {L. K. Kusainova},
     title = {Embedding the weighted {Sobolev} space $W^l_p(\Omega;v)$ in the~space $L_p(\Omega;\omega)$},
     journal = {Sbornik. Mathematics},
     pages = {275--290},
     publisher = {mathdoc},
     volume = {191},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_2_a4/}
}
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L. K. Kusainova. Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the~space $L_p(\Omega;\omega)$. Sbornik. Mathematics, Tome 191 (2000) no. 2, pp. 275-290. http://geodesic.mathdoc.fr/item/SM_2000_191_2_a4/