Geodesic
Continuity of embeddings of weighted Sobolev spaces in Lebesgue spaces on anisotropically irregular domains
Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 271-289

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In our earlier publications, the domains satisfying the flexible $\sigma$-cone condition were classified with respect to an anisotropy parameter $\lambda$. In the present paper we establish the continuity of embeddings of weighted Sobolev spaces in Lebesgue spaces in these classes of domains. For each class of domains with parameter $\lambda\ne(1,\dots,1)$, the theorems obtained are stronger than those in the general case of domains satisfying the flexible $\sigma$-cone condition. 
@article{TRSPY_2010_269_a22,
     author = {B. V. Trushin},
     title = {Continuity of embeddings of weighted {Sobolev} spaces in {Lebesgue} spaces on anisotropically irregular domains},
     journal = {Informatics and Automation},
     pages = {271--289},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a22/}
}
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B. V. Trushin. Continuity of embeddings of weighted Sobolev spaces in Lebesgue spaces on anisotropically irregular domains. Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 271-289. http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a22/