A local regularity for the complex Monge-Ampère equation

Details A local regularity for the complex Monge-Ampère equation A local regularity for the complex Monge-Ampère equation

2010-05-06

arxiv.org/abs/1005.0939v1

Mathematics

Complex Variables

5 pages, submitted

Scientific paper

We prove a local regularity (and a corresponding a priori estmate) for plurisubharmonic solutions of the nondegenerate complex Monge-Amp\'ere equation assuming that their $W^{2,p}$-norm is under control for some $p>n(n-1)$. This condition is optimal. We use in particular some methods developed by Trudinger and an $L^q$-estimate for the complex Monge-Amp\'ere equation due to Ko{\l}odziej.

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