  Flat density cores have been obtained for a limited number of clusters of
galaxies by strong gravitational lensing. This paper explores the possibility
that the degeneracy pressure of fermionic dark matter accounts for the flat top
density profiles. This is a case study of A1689 for which the density profile
has been obtained from the inner region out to 1Mpc by the combination of
strong and weak lensing. In the case that the dark matter consists of the
mixture of degenerate relic neutrinos and collisionless cold dark matter
particles, the acceptable mass range for relic neutrinos is between 1 and 2 eV,
if the ratio of the two kinds of dark matter particles is fixed to its cosmic
value.
