  We study a shape optimization problem for the first eigenvalue of an elliptic
operator in divergence form, with non constant coefficients, over a fixed
domain $\Omega$. Dirichlet conditions are imposed along $\partial \Omega$ and,
in addition, along a set $\Sigma$ of prescribed length ($1$-dimensional
Hausdorff measure). We look for the best shape and position for the
supplementary Dirichlet region $\Sigma$ in order to maximize the first
eigenvalue. The limit distribution of the optimal sets, as their prescribed
length tends to infinity, is characterized via $\Gamma$-convergence of suitable
functionals defined over varifolds: the use of varifolds, as opposed to
probability measures, allows one to keep track of the local orientation of the
optimal sets (which comply with the anisotropy of the problem), and not just of
their limit distribution.
