Imbedding theorems for Sobolev spaces on domains with peak and on Hölder domains

Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators $W_p^l(\Omega)\to L_q(\Omega)$ and $W_p^l(\Omega)\to C(\Omega)\cap L_\infty(\Omega)$ for a domain with an outward peak. More simple sufficient conditions are presented. Applications to the solvability of the Neumann problem for elliptic equations of order $2l$, $ l\ge1$, for a domain with peak are given. An imbedding theorem for Sobolev spaces on Hölder domains is stated.