  In this paper, we study an eigenvalue problem with piecewise constant
coefficients on thin domains with Neumann boundary condition, and we analyze
the asymptotic behavior of each eigenvalue as the domain degenerates into a
certain hypersurface being the set of discontinuities of the coefficients. We
show how the discontinuity of the coefficients and the geometric shape of the
interface affect the asymptotic behavior of the eigenvalues by a using
variational approach.
