  We have investigated the behavior and stability of a Wigner crystal of
rotating dipolar fermions in two dimensions. Using an ansatz wave function for
the ground state of rotating two-dimensional dipolar fermions, which occupy
only partially the lowest Landau level, we study the correlation energy,
elastic moduli and collective modes of Wigner crystals in the lowest Landau
level. We then calculate the mean square of the displacement vector of Wigner
crystals. The critical filling factor, below which the crystalline state is
expected, is evaluated at absolute zero by use of the Lindeman's criterion. We
find that the particle (hole) crystal is locally stable for filling factor is
less than 1/15 (between filling factors 14/15 and 1), where the stable regime
of the crystal is much narrower than the result from Baranov, Fehrmann and
Lewenstein, [Phys. Rev. Lett. 100, 200402 (2008)].
