Asymptotic blow-up analysis for singular Liouville type equations with applications

Next, we refine our blow up analysis to cover a class of planar Liouville type problems (see (1.27)-(1.28) below) arising from the study of Cosmic Strings (cfr. [28,35]). In this context, we are able to distinguish between a single blow-up radial profile and the case of multiple blow-up profiles, typical of non radial solutions. As a consequence we obtain a (radial) symmetry result which is interesting in itself but also contributes towards the “sharp” solvability issue for the planar problem (1.27)-(1.28).