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This is a Quantitative Study study.

October 13, 2025Open Access

Hölder Regularity of Dirichlet Problem For The Complex Monge-Ampère Equation

Key Points

The study establishes that solutions to the Dirichlet problem are globally Hölder continuous.
The methods apply to complex Monge-Ampère equations under specific conditions related to Lp functions.
The analysis involves strict pseudo-convexity and Hölder continuity of boundary data.
Demonstrating these properties may significantly impact the field of complex geometry and PDEs.

Abstract

We study the Dirichlet problem for the complex Monge-Ampère equation on a strictly pseudo-convex domain in Cn or a Hermitian manifold. Under the condition that the right-hand side lies in Lp function and the boundary data are Hölder continuous, we prove the global Hölder continuity of the solution.

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Cite This Study

Hu et al. (Sun,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec0944a https://doi.org/https://doi.org/10.48550/arxiv.2509.11329

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