The complex Monge–Ampère equation on compact Kähler manifolds

By Xiuxiong Chen, Weiyong He. 2010

51 citations recorded by the source corpus.

We consider the complex Monge–Ampère equation on a compact Kähler manifold (M, g) when the right hand side F has rather weak regularity. In particular we prove that estimate of $${\triangle \phi}$$ and the gradient estimate hold when F is in $${W^{1, p_0}}$$ for any p0 > 2n. As an application, we show that there exists a classical solution in $${W^{3, p_0}}$$ for the complex Monge–Ampère equation when F is in $${W^{1, p_0}}$$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/082600f0f46031610b2635f90412cce7cdd1afd0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the constant scalar curvature Kähler metrics (I)—A priori estimates (2017, methodology): “For second order estimate, Chen-He[17] establish an a priori bound on n+∆φ in terms of |∇F |Lp(p > 2n) via integral estimate, in absense of (1.”