  We study a rapidly rotating Bose-Einstein condensate confined to a finite
trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong
coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$
and the rotational velocity by $\Omega$, we evaluate exactly the next to
leading order contribution to the ground state energy in the parameter regime
$|\log\eps|\ll \Omega\ll 1/(\eps^2|\log\eps|)$ with $\eps\to 0$. While the TF
energy includes only the contribution of the centrifugal forces the next order
corresponds to a lattice of vortices whose density is proportional to the
rotational velocity.
