Existence of local sufficiently smooth solutions to 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 $\det \left ( u_{i\overline {j}}\right ) =f\left ( z,u,\nabla u\right )$, $f\geq 0$, in a neighborhood of any point $z_{0}$ where $f\left ( z_{0}\right ) =0$.References
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Additional Information
- Saoussen Kallel-Jallouli
- Affiliation: Faculté des Sciences, Campus Universitaire, 1060 Tunis, Tunisie
- Email: Saoussen.Kallel@fst.rnu.tn
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 3227-3242
- MSC (2000): Primary 32W20
- DOI: https://doi.org/10.1090/S0002-9947-03-03399-3
- MathSciNet review: 2052948