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

• Luca Battaglia ^[1] ; Angela Pistoia ^[2]
  1. [1] Roma Tre University

     Roma Tre University

     Roma Capitale, Italia

     
  2. [2] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1867-1910
• Idioma: inglés
• DOI: 10.4171/rmi/1047
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.