Proceedings of the American Mathematical Society

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

Author(s): Saoussen Kallel-Jallouli
Journal: Proc. Amer. Math. Soc. 131 (2003), 1103-1108.
MSC (2000): Primary 35Mxx, 39B42
Posted: October 15, 2002
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Abstract: We prove the $C^{\infty }$ local solvability of the

-dimensional complex Monge-Ampère equation $\det ( u_{i\overline{j}}) =K\left( z\right) f\left( z,u,\nabla u\right)$ ,

, 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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Mxx, 39B42

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

DOI: 10.1090/S0002-9939-02-06820-X
PII: S 0002-9939(02)06820-X
Keywords: Complex Monge-Amp\`{e}re equation, real principal type symbol
Received by editor(s): March 6, 2001
Posted: October 15, 2002
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2002, American Mathematical Society

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