Dirichlet problem for degenerate elliptic complex Monge-Ampere equation
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We consider the Dirichlet problem
det (∂2u/ ∂zi∂zj) = g(z, u) in Ω, u|∂Ω = φ,
where Ω is a bounded open set of ℂn with regular boundary, g and φ are sufficiently smooth functions, and g is non-negative. We prove that, under additional hypotheses on g and φ, if | detφij - g|Cs* is sufficiently small the problem has a plurisubharmonic solution.
CitationKallel-Jallouli, S. (2004). Dirichlet problem for degenerate elliptic complex Monge-Ampere equation. Electronic Journal of Differential Equations, 2004(48), pp. 1-24.
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