  We prove a Faber-Krahn inequality for the Laplacian with drift under Robin
boundary condition, provided that the $\beta$ parameter in the Robin condition
is large enough. The proof relies on a compactness argument, on the convergence
of Robin eigenvalues to Dirichlet eigenvalues when $\beta$ goes to infinity,
and on a strict Faber-Krahn inequality under Dirichlet boundary condition. We
also show the existence and uniqueness of drifts $v$ satisfying some $L^\infty$
constraints and minimizing or maximizing the principal eigenvalue of
$-\Delta+v\cdot\nabla$ in a fixed domain and with a fixed parameter $\beta>0$
in the Robin condition.
