Revista Matemática Iberoamericana


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Volume 11, Issue 1, 1995, pp. 67–101
DOI: 10.4171/RMI/166

Published online: 1995-04-30

Formulas for approximate solutions of the $\partial \bar{\partial}$-equation in a strictly pseudoconvex domain

Mats Andersson[1] and Hasse Carlsson[2]

(1) Chalmers University of Technology, Gothenburg, Sweden
(2) Chalmers University of Technology, Gothenburg, Sweden

Let $D$ be a bounded strictly pseudoconvex domain in $\mathbb C^n$. We construct approximative solution formulas for the equation $i\partial \bar{\partial}u = \theta$, $\theta$ being an exact (1,1 )-form in $D$. We show that our formulas give simple proofs of known estimates and indicate further applications.

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Andersson Mats, Carlsson Hasse: Formulas for approximate solutions of the $\partial \bar{\partial}$-equation in a strictly pseudoconvex domain. Rev. Mat. Iberoamericana 11 (1995), 67-101. doi: 10.4171/RMI/166