Large solutions to complex Monge-Ampère equations: Existence, uniqueness and asymptotics

Abstract

The authors consider the complex Monge-Ampère equation det\left( {u_{i\bar j} } \right) = ψ(z, u, ∇ u) in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u = ∞ on ∂Ω. Under suitable conditions on ψ, the existence, uniqueness and the exact asymptotic behavior of solutions to boundary blow-up problems for the complex Monge-Ampère equations are established.

Keywords

Complex Monge-Ampère equation / Boundary blow-up / Plurisubharmonic / Pseudoconvex / Asymptotics

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