A unified approach of blow-up phenomena for two-dimensional singular Liouville systems

2016/07/01 by Battaglia, Luca, Pistoia, Angela
#35B40 #35B44 #35J25 #35J57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.00427

Abstract

We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to which blow-up at the origin and whose local mass at the origin is a given quantity depending on the parameters of the system. We can get either finitely many possible blow-up values of the local mass or infinitely many. The blow-up values are produced using an explicit formula which involves Chebyshev polynomials.

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