This article is cited in 8 papers

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

B. V. Trushin

Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, Russia

Abstract: 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.

UDC: 517.518.23

Received in October 2009

 English version: Proceedings of the Steklov Institute of Mathematics, 2010, 269, 265–283

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