We extend the results of a previous paper on the Gross-Pitaevskii description of rotating BoseEinstein condensates in two-dimensional traps to confining potentials of the form V (r) = rs, 2 < s < ∞. Writing the coupling constant as 1/ε we study the limit ε → 0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity Ω tends to infinity as a power of 1/ε. The case of asymptotically homogeneous potentials is also discussed.
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