English

H\"older regularity for solutions to complex Monge-Amp\`ere equations

Complex Variables 2014-03-17 v1

Abstract

We consider the Dirichlet problem for the complex Monge-Amp\`ere equation in a bounded strongly hyperconvex Lipschitz domain in \Cn\C^n. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is C1,1C^{1,1} and the right hand side has a density in Lp(Ω)L^p(\Omega) for some p>1p>1 and prove the H\"older continuity of the solution.

Keywords

Cite

@article{arxiv.1403.3666,
  title  = {H\"older regularity for solutions to complex Monge-Amp\`ere equations},
  author = {Mohamad Charabati},
  journal= {arXiv preprint arXiv:1403.3666},
  year   = {2014}
}
R2 v1 2026-06-22T03:27:11.883Z