Transactions of the American Mathematical Society

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

Author(s): Saoussen Kallel-Jallouli
Journal: Trans. Amer. Math. Soc. 356 (2004), 3227-3242.
MSC (2000): Primary 32W20
Posted: December 12, 2003
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Abstract: We prove the $C^{\infty }$ local solvability of the

-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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