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arXiv · 2205.13096

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

Arunima Bhattacharya·Connor Mooney·Ravi Shankar
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Abstract

In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$. Combined with the a priori interior Hessian estimates proved in [Bha21, Bha22], this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.

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Arunima Bhattacharya, Connor Mooney, Ravi Shankar. 2022-05-26. Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase. https://arxiv.org/abs/2205.13096

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