Abstract:We study the stiff spectral Neumann problem for the Laplace operator in a smooth bounded domain Ω ⊂ R d which is divided into two subdomains: an annulus Ω1 and a core Ω0. The density and the stiffness constants are of order ε −2m and ε −1 in Ω0, while they are of order 1 in Ω1. Here m ∈ R is fixed and ε > 0 is small. We provide asymptotics for the eigenvalues and the corresponding eigenfunctions as ε → 0 for any m. In dimension 2 the case when Ω0 touches the exterior boudary ∂Ω and Ω1 gets two cusps at a point… Show more
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