Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Xingchen Zhou

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arXiv · 2311.13867

Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Xingchen Zhou

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Abstract

We establish a prior interior $C^{1,1}$ estimates for convex solutions and supercritical phase solutions to the Lagrangian mean curvature equation with sharp Lipschitz phase. Counter-examples exist when the phase is H\"{o}lder continuous but not Lipschitz. As an application we obtain interior $C^{2,\alpha}$ regularity for $C^0$ viscosity solutions on the first phase interval $((n-2)\frac\pi2,n\frac\pi2)$.

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Xingchen Zhou. 2023-11-23. Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase. https://arxiv.org/abs/2311.13867

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