H\"older Regularity of Dirichlet Problem For The Complex Monge-Amp\`ere Equation
Complex Variables
2026-03-10 v3 Analysis of PDEs
Differential Geometry
Abstract
We study the Dirichlet problem for the complex Monge-Amp\`ere equation on a strictly pseudoconvex domain in Cn or a Hermitian manifold. Under the condition that the right-hand side lies in Lp function and the boundary data are H\"older continuous, we prove the global H\"older continuity of the solution.
Keywords
Cite
@article{arxiv.2509.11329,
title = {H\"older Regularity of Dirichlet Problem For The Complex Monge-Amp\`ere Equation},
author = {Yuxuan Hu and Bin Zhou},
journal= {arXiv preprint arXiv:2509.11329},
year = {2026}
}
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16 pages, 0 figures