A local regularity for the complex Monge-Amp\`ere equation

Zbigniew Blocki; Slawomir Dinew

A local regularity for the complex Monge-Amp\`ere equation

Complex Variables 2010-05-07 v1

Authors: Zbigniew Blocki , Slawomir Dinew

Abstract

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.

Keywords

complex monge-ampère equation regularity for elliptic equations regularity of solutions

Cite

@article{arxiv.1005.0939,
  title  = {A local regularity for the complex Monge-Amp\`ere equation},
  author = {Zbigniew Blocki and Slawomir Dinew},
  journal= {arXiv preprint arXiv:1005.0939},
  year   = {2010}
}

Comments

5 pages, submitted

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