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

B. V. Trushin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 271-289.

Résumé

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.

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