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


Author: Saoussen Kallel-Jallouli
Journal: Proc. Amer. Math. Soc. 131 (2003), 1103-1108
MSC (2000): Primary 35Mxx, 39B42
DOI: https://doi.org/10.1090/S0002-9939-02-06820-X
Published electronically: October 15, 2002
MathSciNet review: 1948100
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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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Additional Information

Saoussen Kallel-Jallouli
Affiliation: Faculté des Sciences de Tunis, Mathématiques, Campus Universitaire, 1060 Tunis, Tunisie
Email: Saoussen.Kallel@fst.rnu.tn

DOI: https://doi.org/10.1090/S0002-9939-02-06820-X
Keywords: Complex Monge-Amp\`{e}re equation, real principal type symbol
Received by editor(s): March 6, 2001
Published electronically: October 15, 2002
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

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