Imbedding theorems for Sobolev spaces on domains with peak and on H\"older domains

V. G. Maz'ya ; S. V. Poborchi

Algebra i analiz, Tome 18 (2006) no. 4, pp. 95-126.

Résumé

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.

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