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 $\epsilon \to 0$. 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.