  This is a continuation of the paper 'Symmetry breaking and other phenomena in
the optimization of eigenvalues for composite membranes' by S. Chanillo, D.
Grieser, M. Imai, K. Kurata, and I. Ohnishi.
  Again, we consider the following eigenvalue optimization problem: Given a
bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in
[0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first
Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as
possible.
  In this paper we focus on the study of the free boundary of optimal solutions
on general domains.
