  We study the rotation of a $^{87}$Rb Bose-Einstein condensate confined in a
magnetic trap to which a focused, off resonant gaussian laser beam is
superimposed. The confining potential is well approximated by the sum of a
quadratic and a quartic term which allows to increase the rotation frequency of
the gas above the trap frequency. In this fast rotation regime we observe a
dramatic change in the appearance of the quantum gas. The vortices which were
easily detectable for a slower rotation become much less visible, and their
surface density is well below the value expected for this rotation frequency
domain. We discuss some possible tracks to account for this effect.
