Journal d’Analyse Mathématique

, Volume 90, Issue 1, pp 303–335

Positive versus free boundary solutions to a singular elliptic equation

  • Juan Dávila
  • Marcelo Montenegro

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.

Copyright information

© Hebrew University of Jerusalem 2003

Authors and Affiliations

  • Juan Dávila
    • 1
  • Marcelo Montenegro
    • 2
  1. 1.Department of Mathematics RutgersUniversity 110 FrelinghuysenUSA
  2. 2.Departamento de MatemáticaUniversidade Estadual de CampinasCampinasBrasil