  We consider the eigenvalues of an elliptic operator for systems with bounded,
measurable, and symmetric coefficients. We assume we have two non-empty, open,
disjoint, and bounded sets and add a set of small measure to form the perturbed
domain. Then we show that the Dirichlet eigenvalues corresponding to the family
of perturbed domains converge to the Dirichlet eigenvalues corresponding to the
unperturbed domain. Moreover, our rate of convergence is independent of the
eigenvalues. In this paper, we consider the Lam\'{e} system, systems which
satisfy a strong ellipticity condition, and systems which satisfy a
Legendre-Hadamard ellipticity condition.

Analysis of PDEs