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William Alexandre
$C^k$-estimates for the $\overline{\partial }$-equation on concave domains of finite type
Annales de la faculté des sciences de Toulouse Sér. 6, 15 no. 3 (2006), p. 399-426, doi: 10.5802/afst.1126
Article PDF | Reviews MR 2246411

Résumé - Abstract

$C^k$ estimates for convex domains of finite type in $\mathbb{C}^n$ are known from [7] for $k=0$ and from [2] for $k>0$. We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching $z$ and $\zeta $ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work. To overcome this problem we have to alter the Diederich-Fornæss support function. Also we have to take care of the so generated residual term in the homotopy formula.

Bibliography

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