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arXiv · 2511.03426

Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation

Guoqing Cui·Ling Wang·Bin Zhou
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Abstract

In this paper, we establish local potential estimates and H\"older estimates for solutions of linearized Monge-Amp\`ere equations with the right-hand side being a signed measure, under suitable assumptions on the data. In particular, the interior H\"older estimate holds for an inhomogeneous linearized Monge-Amp\`ere equation with right-hand side being the nonnegative divergence of a bounded vector field in all dimensions. As an application, we give a new approach for the interior estimate of the singular Abreu equation.

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Guoqing Cui, Ling Wang, Bin Zhou. 2025-11-05. Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation. https://arxiv.org/abs/2511.03426

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