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
Article

Abstract

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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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

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