  In this paper we consider the minimizing sequence for some energy functional
of an elliptic equation associated with the mean field limit of the point
vortex distribution one-sided Borel probability measure. If such a sequence
blows up, we derive some estimate which is related to the behavior of solution
near the blow-up point. Moreover, we study the two intensities case to consider
the sufficient condition for this estimate. Our main results are new for the
standard mean field equation as well.
