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arXiv · 2511.18605

A necessary and sufficient condition for H\"{o}lder-class solutions to the complex Monge--Amp\`{e}re equation

Annapurna Banik
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Abstract

We provide a necessary and sufficient condition for the existence of H\"{o}lder continuous solutions to the complex Monge--Amp\`{e}re equation on bounded domains in $\mathbb{C}^n$. This condition is motivated by a paper by S.-Y. Li. We also prove a result on the regularity of solutions to the complex Monge--Amp\`{e}re equation on general $B$-regular domains in $\mathbb{C}^n$.

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Annapurna Banik. 2025-11-23. A necessary and sufficient condition for H\"{o}lder-class solutions to the complex Monge--Amp\`{e}re equation. https://arxiv.org/abs/2511.18605

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