复杂蒙日-安培方程的渐近性和收敛性

IF 2.4 1区数学 Q1 MATHEMATICS

Annals of Pde Pub Date : 2024-04-02 DOI:10.1007/s40818-024-00171-2

Qing Han, Xumin Jiang

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引用次数: 0

摘要

我们研究了在\(\mathbb {C}^n\) 中严格伪凸域上的完整凯勒-爱因斯坦度量的渐近性，并推导出相应蒙日-安培方程的解的收敛定理。如果只有部分边界是解析的，解就会满足切向导数的 Gevrey 型估计。模型线性化方程的反例表明，复数 Monge-Ampère 方程不存在局部收敛定理。

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Asymptotics and Convergence for the Complex Monge-Ampère Equation

We study the asymptotics of complete Kähler-Einstein metrics on strictly pseudoconvex domains in \(\mathbb {C}^n\) and derive a convergence theorem for solutions to the corresponding Monge-Ampère equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampère equation.

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来源期刊

Annals of Pde Mathematics-Geometry and Topology

CiteScore

3.70

自引率

3.60%

发文量