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<\infty. Writing the coupling constant as 1/\epsilon^2, we study the limit \epsilon→0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity tends to infinity as a power of 1/\epsilon. The case of asymptotically homogeneous potentials is also discussed.