The complex Monge-Ampere equation on compact Kaehler manifolds

Details The complex Monge-Ampere equation on compact Kaehler manifolds The complex Monge-Ampere equation on compact Kaehler manifolds

2010-04-04

arxiv.org/abs/1004.0543v2

Mathematics

Differential Geometry

17 pages; references are corrected and added

Scientific paper

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

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