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

Author: Saoussen Kallel-Jallouli
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3227-3242
MSC (2000): Primary 32W20
Published electronically: December 12, 2003
MathSciNet review: 2052948
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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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Additional Information

Saoussen Kallel-Jallouli
Affiliation: Faculté des Sciences, Campus Universitaire, 1060 Tunis, Tunisie

Received by editor(s): January 15, 2002
Received by editor(s) in revised form: February 5, 2003, and March 19, 2003
Published electronically: December 12, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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