On the complex Monge-Ampère equation in the ball of \(\mathbb{C}^n)\) (Q1124045)
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scientific article; zbMATH DE number 4111170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the complex Monge-Ampère equation in the ball of \(\mathbb{C}^n)\) |
scientific article; zbMATH DE number 4111170 |
Statements
On the complex Monge-Ampère equation in the ball of \(\mathbb{C}^n)\) (English)
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1989
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On considère le problème de Dirichlet: \[ (dd^cu)^ n=0\quad\text{ dans }B;\quad u|_{\partial B}=\phi \] où \(B\) désigne la boule unité de \(\mathbb C^n\). Nous donnons une démonstration simple du fait que si \(\phi \in C^{1,1}(\partial B)\), alors \(u\in C^{1,1}(B)\); de plus la croissance du coefficient de Lipschitz de la différentielle de \(u\) est contrôlée par l'inverse de la distance au bord.
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Dirichlet problem
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regularity
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boundary dependence
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coefficient growth
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