On the shape of blow-up solutions to a mean field equation

We analyse the structure of non-radial N-point blow up solutions sequences for the Liouville type equation on the two-dimensional unit disc, In the case N = 1, 2, we provide necessary and sufficient conditions for the existence of blow up solutions and, in the spirit of Chen and Lin (2001 Ann. Inst. H. Poincaré. Anal. Non Linéare 18 271), 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 λ − 8π > 0.