Existence of local sufficiently smooth solutions to the complex Monge-Ampère equation

Kallel-Jallouli, Saoussen

doi:10.1090/S0002-9947-03-03399-3

Existence of local sufficiently smooth solutions to the complex Monge-Ampère equation
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Trans. Amer. Math. Soc. 356 (2004), 3227-3242 Request permission

Abstract:

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

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