2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210782We 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 $Ω$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime $|\log\eps|\ll Ω\ll 1/(\eps^2|\log\eps|)$ 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.19 pages, LaTeX; typos corrected, clarifying remarks added, some rearrangements in the textMathematical PhysicsOther Condensed Matter35Q55,47J30,76M23text