  We study the fast rotation limit for a Bose-Einstein condensate in a
quadratic plus quartic confining potential within the framework of the two
dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to
infinity with a proper scaling of the other parameters in the model, a linear
limit problem appears for which we are able to derive precise energy estimates.
We prove that the energy and density asymptotics of the problem can be obtained
by minimizing a simplified one dimensional energy functional. In the case of a
fixed coupling constant we also prove that a giant vortex state appears. It is
an annulus with pure irrotational flow encircling a central low-density hole
around which there is a macroscopic phase circulation.
