  We prove the existence of an open set minimizing the first Dirichlet
eigenvalue of an elliptic operator with bounded, measurable coefficients, over
all open sets of a given measure. Our proof is based on a free boundary
approach: we characterize the eigenfunction on the optimal set as the minimizer
of a penalized functional, and derive openness of the optimal set as a
consequence of a H\"older estimate for the eigenfunction. We also prove that
the optimal eigenfunction grows at most linearly from the free boundary, i.e.
it is Lipschitz continuous at free boundary points.
