Electron. J. Diff. Equ., Vol. 2013 (2013), No. 62, pp. 1-10.

Global solutions with $\mathcal{C}^k$-estimates for $\bar{\partial}$-equations on q-concave intersections

Shaban Khidr, Moulay-Youssef Barkatou

We construct a global solution to the $\bar{\partial}$-equation with $\mathcal{C}^k$-estimates on q-concave intersections in $\mathbb{C}^n$. Our main tools are integral formulas.

Submitted November 20, 2012. Published February 28, 2013.
Math Subject Classifications: 32A26, 32F10, 32W05, 32W10.
Key Words: $\bar{\partial}$-equation; q-convexity; q-concave intersections; $\mathcal{C}^k$-estimates.

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Shaban Khidr
Mathematics Department, Faculty of Science
King Abdelaziz University
North Jeddah, Jeddah, Saudi Arabia
email: skhidr@kau.edu.sa
Moulay-Youssef Barkatou
Laboratoire de Mathématiques et Applications
UMR 7348 CNRS - Université de Poitiers, Téléport 2
11, Boulevard Marie et Pierre Curie, BP 30179
86962 Futuroscope Chasseneuil Cedex, France
email: youssef.barkatou@math.univ-poitiers.fr

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