Existence of $C^\{\infty \}$ local solutions of the complex Monge-Ampère equation
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- by Saoussen Kallel-Jallouli PDF
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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 $dK\left ( z_{0}\right ) \neq 0$.References
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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
- Received by editor(s): March 6, 2001
- Published electronically: October 15, 2002
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1948100