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 ofuλ even in the presence of the free boundary.
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Supported in part by H. J. Sussmann’s NSF Grant DMS01-03901.
Supported by FAPESP. He also thanks Rutgers University.
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Dávila, J., Montenegro, M. Positive versus free boundary solutions to a singular elliptic equation. J. Anal. Math. 90, 303–335 (2003). https://doi.org/10.1007/BF02786560
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DOI: https://doi.org/10.1007/BF02786560