Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry

• Azahara DelaTorre ^[1] ; María del Mar González ^[2]
  1. [1] University of Fribourg

     University of Fribourg

     Friburgo, Suiza

     
  2. [2] Universidad Autónoma de Madrid

     Universidad Autónoma de Madrid

     Madrid, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1645-1678
• Idioma: inglés
• DOI: 10.4171/rmi/1038
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider radial solutions with an isolated singularity for a semilinear equation involving the fractional Laplacian. In conformal geometry, this is equivalent to the study of singular metrics with constant fractional curvature (singular fractional Yamabe problem). Our main ideas are: first, to set up the problem into a natural geometric framework; and second, to reduce the problem to a non-local ODE for which we are able to perform some kind of phase portrait study.