On the shape of blowup solutions to a mean field equation

We analyze the structure of non radial $N$-point blow up solutions sequences for the Liouville type equation on the two dimensional unit disk, $$ -\lapl u(x)=\la \dfrac{\e{u(x)}}{\inb\e{u(x)} \dx}\;\;\mbox{in}\;\; D, \;\;u(x)=0\;\;\mbox{on}\;\; D.$$ In case $N=1,2$, we provide necessary and sufficient conditions for the existence of blow up solutions and, in the same spirit of \cite{cl1}, prove their axial symmetry with respect to the diameter joining the maximum points. Finally, we prove that a non radial one point blow up solution exists only if $\la-8\pi>0$.