Sergei Poborchi

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

Necessary and sufficient conditions are obtained for the continuity and compactness of the imbedding operators W l p(Ω) → Lq(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 Hölder domains is stated. §

On Solvability of Integral Equations for Harmonic Single Layer Potential on the Boundary of a Domain with Cusp

We present solvability theorems for boundary integral equations of the Dirichlet and the Neumann problems on a multi–dimensional domain with cusp which were established in recent joint papers by V.G. Maz’ya and the author.

Sobolev spaces for domains with cusps

This paper presents extension, embedding and trace theorems for Sobolev spaces for domains with cusps, which have been established in joint works by Maz’ya and the author during the last years.