Continuity of embeddings of weighted Sobolev spaces in Lebesgue spaces on anisotropically irregular domains

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.