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

Luca Battaglia, Angela Pistoia

• We consider generic 2×2 singular Liouville systems where Ω∋0 is a smooth bounded domain in R 2 possibly having some symmetry with respect to the origin, δ0is the Dirac mass at 0, λ1 ,λ 2 are small positive parameters and a,b,α 1 ,α 2 >0.

  We construct a family of solutions to (⋆) which blow up at the origin as λ 1 →0 and λ 2 →0 and whose local mass at the origin is a given quantity depending on a,b,α 1 ,α 2.

  In particular, if ab<4 we get finitely many possible blow-up values of the local mass, whereas if ab≥4 we get infinitely many. The blow-up values are produced using an explicit formula which involves Chebyshev polynomials.