Khidr, Shaban; Barkatou, Moulay-Youssef Global solutions with \(C^k\)-estimates for bar-\(d\)-equations on \(q\)-concave intersections. (English) Zbl 1287.32002 Electron. J. Differ. Equ. 2013, Paper No. 62, 10 p. (2013). Summary: 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. MSC: 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) 32F10 \(q\)-convexity, \(q\)-concavity 32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators Keywords:\(\overline\partial\)-equation; \(q\)-convexity; \(q\)-concave intersections; \(\mathcal{C}^k\)-estimates PDFBibTeX XMLCite \textit{S. Khidr} and \textit{M.-Y. Barkatou}, Electron. J. Differ. Equ. 2013, Paper No. 62, 10 p. (2013; Zbl 1287.32002) Full Text: EMIS