  We investigate the vortex patterns appearing in a two-dimensional annular
Bose-Einstein condensate rotating in a quadratic plus quartic confining
potential. We show that in the limit of small anharmonicity the
Gross-Pitaevskii energy can be minimized amongst the Lowest Landau Level wave
functions and use this particular form to get theoretical results in the spirit
of [A. Aftalion X. Blanc F. Nier, Phys. Rev. A 73, 011601(R) (2006)]. In
particular, we show that the vortex pattern is infinite but not uniform. We
also compute numerically the complete vortex structure: it is an Abrikosov
lattice strongly distorted near the edges of the condensate with multiply
quantized vortices appearing at the center of the trap.
