  We derive a uniformly frustrated $XY$ model that describes two-dimensional
Josephson-junction arrays consisting of rotating Bose-Einstein condensates
trapped by both a harmonic trap and a corotating deep optical lattice. The
harmonic trap makes the coupling constant of the model have a nonuniform
parabolic dependance. We study the ground state through Monte Carlo simulations
in a wide range of the frustration parameter $f$, revealing a rich variety of
vortex patterns.
