Let Ω be a C 4 -smooth bounded pseudoconvex domain in 2 . We show that if the ∂ ¯ -Neumann operator N 1 is compact on L ( 0 , ) then embedding J : D o m ∩ ∗ → p -regular for all ⩽ < ∞

We study the stiff spectral Neumann problem for Laplace operator in a smooth bounded domain Ω ⊂ R d which is divided into two subdomains: an annulus 1 and core 0 . The density stiffness constants are of order ε − 2 m , while they Here ∈ fixed &gt; small. provide asymptotics eigenvalues corresponding eigenfunctions as → any m. In dimension case when touches exterior boundary ∂ gets cusps at poin...