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

Abstract

We study the Dirichlet problem for the complex Monge-Amp\`ere 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 H\"older continuous, we prove the global H\"older continuity of the solution.

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