Conditions for Embeddings of Sobolev Spaces on a Domain with Anisotropic Peak

For a domain $G\subset \mathbb R^n$ with an anisotropic peak, we construct integral representations of functions in terms of derivatives and establish conditions for the embedding $W_p^s(G)\subset L_q(G)$ of the Sobolev space in the Lebesgue space for $1\leq p<q\le \infty $.