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Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase
Abstract
Let n≥3. We prove a priori interior gradient estimate for the Lagrangian mean curvature equation ∑i=1narctanλi(D2u)=θ(x) under the critical and supercritical phase condition θ≥ (n−2)π/2, assuming only that the Lipschitz norm of the prescribed phase is bounded.
Related
- Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides
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- Interior gradient estimates for mean curvature equations on Riemannian manifolds
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BibTeX
@misc{chen2026gradient,
title = {{Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase}},
author = {Ruosi Chen and Xingchen Zhou and Ruixuan Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06692},
eprint = {2609.06692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06692},
}
RIS
TY - UNPB
TI - Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase
AU - Ruosi Chen
AU - Xingchen Zhou
AU - Ruixuan Zhu
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06692
UR - https://arxiv.org/abs/2609.06692
AB - Let n≥3. We prove a priori interior gradient estimate for the Lagrangian mean curvature equation ∑_i=1^narctanλ_i(D^2u)=θ(x) under the critical and supercritical phase condition θ≥ (n−2)π/2, assuming only that the Lipschitz norm of the prescribed phase is bounded.
ER -