Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands

Abstract

We consider a Dirichlet spectral problem for a second order differential operator, with piecewise constant coefficients, in a domain [Omega] in the plane R2. Here [ ], where [Omega] is a fixed bounded domain with boundary , is a curvilinear band of width O(epsilon), and . The density and stiffness constants are of order mt and t respectively in this band, while they are of order 1 in ; t1, m>2, and is a small positive parameter. We address the asymptotic behavior, as 0, for the eigenvalues and the corresponding eigenfunctions. In particular, we show certain localization effects for eigenfunctions associated with low frequencies. This is deeply involved with the extrema of the curvature of