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

Ruosi Chen, Xingchen Zhou, Ruixuan Zhu

Let $n\ge 3$. We prove a priori interior gradient estimate for the Lagrangian mean curvature equation \[ \sum_{i=1}^n\arctanλ_i(D^2u)=θ(x) \] under the critical and supercritical ph…