On the $C^{2,α}$-regularity of the complex Monge–Ampère equation
On the $C^{2,α}$-regularity of the complex Monge–Ampère equation
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关于复数Monge-Ampère方程的$C^{2,α}$-正则性
DOI：
10.4310/mrl.2012.v19.n4.a16
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发表时间：
2012
影响因子：
1
通讯作者：
Yu Wang
中科院分区：
文献类型：
--
作者：
Yu Wang
在Δ u有界的条件下，证明了方程det（uk <$j）= f，f1/n ∈ C，f ≥ λ的解u的C2，α-正则性.我们的结果解决了文献[12]中遗留的一个正则性问题（另见[13]）。证明是基于一个减少复杂的蒙赫-安培方程的贝尔曼型方程，完全非线性一致椭圆方程的正则性理论可以应用。
We prove the C2,α-regularity of the solution u to the equation det(uk̄j) = f, f 1/n ∈ C, f ≥ λ, under the assumption that Δu is bounded from above. Our result settles one of the regularity problems left open in the paper [12] (see also [13]). The proof is based on a reduction of the complex Monge–Ampère equation to a Bellman-type equation, to which the regularity theory of fully nonlinear uniformly elliptic equations can be applied.