Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation
Analysis of PDEs
2025-11-06 v1
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.
Keywords
Cite
@article{arxiv.2511.03426,
title = {Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation},
author = {Guoqing Cui and Ling Wang and Bin Zhou},
journal= {arXiv preprint arXiv:2511.03426},
year = {2025}
}