Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds

• Ilkka Holopainen ^[1] ; Jaime B. Ripoll ^[2]
  1. [1] University of Helsinki

     University of Helsinki

     Helsinki, Finlandia

     
  2. [2] Universidade Federal do Rio Grande do Sul

     Universidade Federal do Rio Grande do Sul

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 3, 2015, págs. 1107-1129
• Idioma: inglés
• DOI: 10.4171/RMI/864
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show, by modifying Borbély’s example, that there are 3-dimensional Cartan–Hadamard manifolds M, with sectional curvatures ≤ −1, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.