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arXiv · 2609.06692

Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase

Ruosi Chen·Xingchen Zhou·Ruixuan Zhu
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Abstract

Let $n\ge3$. We prove a priori interior gradient estimate for the Lagrangian mean curvature equation \[ \sum_{i=1}^n\arctan\lambda_i(D^2u)=\theta(x) \] under the critical and supercritical phase condition $\theta\ge (n-2)\pi/2$, assuming only that the Lipschitz norm of the prescribed phase is bounded.

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Ruosi Chen, Xingchen Zhou, Ruixuan Zhu. 2026-09-06. Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase. https://arxiv.org/abs/2609.06692

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