Positive versus free boundary solutions to a singular elliptic equation |
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| Authors: | Juan Dávila Marcelo Montenegro |
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| Affiliation: | (1) Department of Mathematics Rutgers, University 110 Frelinghuysen, Rd PISCATAWAY, 08854-8019, NJ, USA;(2) Departamento de Matemática, Universidade Estadual de Campinas, IMECC Caixa Postal 6065, CEP 13083-970 Campinas, SP, Brasil |
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| 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. Supported in part by H. J. Sussmann’s NSF Grant DMS01-03901. Supported by FAPESP. He also thanks Rutgers University. |
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