Journal d’Analyse Mathématique

, Volume 90, Issue 1, pp 303–335

Positive versus free boundary solutions to a singular elliptic equation


  • Juan Dávila
    • Department of Mathematics RutgersUniversity 110 Frelinghuysen
  • Marcelo Montenegro
    • Departamento de MatemáticaUniversidade Estadual de Campinas

DOI: 10.1007/BF02786560

Cite this article as:
Dávila, J. & Montenegro, M. J. Anal. Math. (2003) 90: 303. doi:10.1007/BF02786560


The equation-δu = χ uo(-1/uΒ + λf (x, u)) in Ω with Dirichlet boundary condition on ∂Ω has a maximal solution uλ ≥0 for every λ 0. For λ less than a constant λ*, the solution vanishes inside the domain; and for λ λ*, the solution is positive. We obtain optimal regularity of even in the presence of the free boundary.

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© Hebrew University of Jerusalem 2003