%0 Journal Article
%T A local regularity for the complex Monge-Amp¨¨re equation
%A Zbigniew Blocki
%A Slawomir Dinew
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1005.0939v1