Complex Monge-Amp\`ere equation in strictly pseudoconvex domains

Hoang-Son Do; Thai Duong Do; Hoang Hiep Pham

Complex Monge-Amp\`ere equation in strictly pseudoconvex domains

Complex Variables 2018-08-23 v1

Authors: Hoang-Son Do , Thai Duong Do , Hoang Hiep Pham

Abstract

We study the complex Monge-Amp\`ere equation $(dd^c u)^n=\mu$ in a strictly pseudoconvex domain $\Omega$ with the boundary condition $u=\varphi$ , where $\varphi\in C(\partial\Omega)$ . We provide a non-trivial sufficient condition for continuity of the solution $u$ outside "small sets".

Keywords

complex monge-ampère equation pseudoconvex domains

Cite

@article{arxiv.1808.07264,
  title  = {Complex Monge-Amp\`ere equation in strictly pseudoconvex domains},
  author = {Hoang-Son Do and Thai Duong Do and Hoang Hiep Pham},
  journal= {arXiv preprint arXiv:1808.07264},
  year   = {2018}
}

Comments

9 pages

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