Existence of $C^\{\infty \}$ local solutions of the complex Monge-Ampère equation

Saoussen Kallel-Jallouli
2002 Proceedings of the American Mathematical Society  
We prove the C ∞ local solvability of the n-dimensional complex Monge-Ampère equation det(u ij ) = K (z) f (z, u, ∇u), f > 0, in a neighborhood of any point z 0 where K (z 0 ) = 0 but dK (z 0 ) = 0.
doi:10.1090/s0002-9939-02-06820-x fatcat:jl3yiub3jzfw5mgobcmf3zyez4