Analysis demonstrates global Hölder continuity of solutions in pseudo-convex domains and Hermitian manifolds.
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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Hu et al. (2025) studied this question.
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