Expansion of the energy of the ground state of the Gross-Pitaevskii equation in the Thomas-Fermi limit

From the asymptotic expansion of the ground state of the Gross–Pitaevskii equation in the Thomas–Fermi limit given by Gallo and Pelinovsky [GP], we infer an asymptotic expansion of the kinetic, potential and total energy of the ground state. In particular, we give a rigorous proof of the expansion of the kinetic energy calculated by Dalfovo, Pitaevskii and Stringari [DPS] in the case where the space dimension is 3. Moreover, we calculate one more term in this expansion, and we generalize the result to space dimensions 1 and 2.