H\"older Regularity of Dirichlet Problem For The Complex Monge-Amp\`ere Equation

Yuxuan Hu; Bin Zhou

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arXiv · 2509.11329

H\"older Regularity of Dirichlet Problem For The Complex Monge-Amp\`ere Equation

Yuxuan Hu·Bin Zhou

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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.

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Yuxuan Hu, Bin Zhou. 2025-09-14. H\"older Regularity of Dirichlet Problem For The Complex Monge-Amp\`ere Equation. https://arxiv.org/abs/2509.11329

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