  We apply Dynamical Mean-Field Theory to strongly interacting fermions in an
inhomogeneous environment. With the help of this Real-Space Dynamical
Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of
repulsively interacting fermions with spin 1/2 in a harmonic potential. Within
R-DMFT, antiferromagnetic order is found to be stable in spatial regions with
total particle density close to one, but persists also in parts of the system
where the local density significantly deviates from half filling. In systems
with spin imbalance, we find that antiferromagnetism is gradually suppressed
and phase separation emerges beyond a critical value of the spin imbalance.
