Existence of 𝐶^{{}∞} local solutions of the complex Monge-Ampère equation

Kallel-Jallouli, Saoussen

doi:10.1090/S0002-9939-02-06820-X

Existence of $C^\{\infty \}$ local solutions of the complex Monge-Ampère equation
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Proc. Amer. Math. Soc. 131 (2003), 1103-1108 Request permission

Abstract:

We prove the $C^{\infty }$ local solvability of the $n$-dimensional complex Monge-Ampère equation $\det ( u_{i\overline {j}}) =K\left ( z\right ) f\left ( z,u,\nabla u\right )$, $f>0$, in a neighborhood of any point $z_{0}$ where $K\left ( z_{0}\right ) =0$ but $dK\left ( z_{0}\right ) \neq 0$.

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