arXiv subjects

Guoqing Cui

Publications and source records attributed to Guoqing Cui.

2 recordsLinked to original sources

arXiv2026

Gradient potential estimates for linearized Monge-Amp\`ere equations

This paper establishes a pointwise gradient potential estimate for solutions to linearized Monge-Amp\`ere equations and derives a modulus of continuity estimate for the gradient in terms of the associated section adapted potential. As applications, we obtain a sufficient criterion for the continuity of the gradient, local BMO and VMO estimates for the gradient with respect to Monge-Amp\`ere sections, and a local $C^{1,\gamma}$ regularity criterion.

math.AP↗

arXiv2025

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

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.

math.AP↗