The stiff Neumann problem: Asymptotic specialty and “kissing” domains

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 > small. provide asymptotics eigenvalues corresponding eigenfunctions as → any m. In dimension case when touches exterior boundary ∂ gets cusps at point O included consideration. possibility to apply same asymptotic procedure “smooth” based on structure vicinity irregular part. full series x solutions mixed value cuspidal given.