Rapidly rotating Bose-Einstein condensates in homogeneous traps

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r)=r(s), 2 < s 0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity Omega tends to infinity as a power of 1/epsilon. The case of asymptotically homogeneous potentials is also discussed.