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We investigate the phase separation of resonantly interacting fermions in atrap with imbalanced spin populations, both at zero and at finite temperatures.We directly minimize the thermodynamical potential under the local densityapproximation instead of using the gap equation, as the latter may giveunstable solutions. On the BEC side of the resonance, one may cross threedifferent phases from the trap center to the edge; while on the BCS side or atresonance, typically only two phases show up. We compare our results with therecent experiment, and the agreement is remarkable.Comment: 4 pages, 3 figures, replaced with the published versio

Trapped fermions across a Feshbach resonance with population imbalance