![](https://crypto4nerd.com/wp-content/uploads/2024/02/1707656495_15EyQc-m3dOkCJyMbdLfL2w.jpeg)
- Hessian estimates for special Lagrangian equation by doubling(arXiv)
Author : Ravi Shankar
Abstract : New, doubling proofs are given for the interior Hessian estimates of the special Lagrangian equation. These estimates were originally shown by Chen-Warren-Yuan in CPAM 2009 and Wang-Yuan in AJM 2014. This yields a higher codimension analogue of Korevaar’s 1987 pointwise proof of the gradient estimate for minimal hypersurfaces, without using the Michael-Simon mean value inequality.
2. Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase(arXiv)
Author : Xingchen Zhou
Abstract : We establish a prior interior C1,1 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 Hölder continuous but not Lipschitz. As an application we obtain interior C2,α regularity for C0 viscosity solutions on the first phase interval ((n−2)π2,nπ2)