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

摘要

Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators W~L_p(Ω)→L_q(Ω) and W~l_p(Ω)→C(Ω)∩L_∞(Ω) 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≥1 , for a domain with peak are given. An imbedding theorem for Sobolev spaces on H?lder domains is stated.