# Hessian estimates for Lagrangian mean curvature equation

@article{Bhattacharya2021HessianEF,
title={Hessian estimates for Lagrangian mean curvature equation},
author={Arunima Bhattacharya},
journal={Calculus of Variations and Partial Differential Equations},
year={2021}
}
• A. Bhattacharya
• Published 29 May 2020
• Mathematics
• Calculus of Variations and Partial Differential Equations
In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.
4 Citations
Regularity for convex viscosity solutions of Lagrangian mean curvature equation
• Mathematics
• 2020
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Holder continuous second derivatives.
A note on the two dimensional Lagrangian mean curvature equation
• Arunima Bhattacharya
• Mathematics
• 2021
In this note, we use Warren-Yuan’s [WY09] super isoperimetric inequality on the level sets of subharmonic functions, which is available only in two dimensions, to derive a modified Hessian bound forExpand
Optimal regularity for Lagrangian mean curvature type equations
• Mathematics
• 2020
We classify regularity for a class of Lagrangian mean curvature type equations, which includes the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvatureExpand
The Dirichlet problem for Lagrangian mean curvature equation
In this paper, we solve the Dirichlet problem with continuous boundary data for Lagrangian mean curvature equation on a uniformly convex, bounded domain in $\mathbb{R}^n$.

#### References

SHOWING 1-10 OF 47 REFERENCES
Regularity for convex viscosity solutions of Lagrangian mean curvature equation
• Mathematics
• 2020
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Holder continuous second derivatives.
Hessian estimates for the sigma-2 equationin dimension 3
• Mathematics
• 2009
We derive a priori interior Hessian estimates for the special Lagrangian equation � 2 D1 in dimension3. c � 2008 Wiley Periodicals, Inc.
A Priori Estimate for Convex Solutions to Special Lagrangian Equations and Its Application
• Mathematics
• 2009
We derive a priori interior Hessian estimates for special Lagrangian equations when the potential is convex. When the phase is very large, we show that continuous viscosity solutions are smooth inExpand
Regularity for convex viscosity solutions of special Lagrangian equation
• Mathematics
• 2019
We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.
Interior Hessian estimates for Sigma-2 equations in dimension three
We prove a priori interior C2 estimate for \sigma_2 = f in R3, which generalizes Warren-Yuan's result.
A Bernstein problem for special Lagrangian equations
We derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimalExpand
Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase
• Mathematics
• 2008
<abstract abstract-type="TeX"><p>We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. GradientExpand
Singular Solution to Special Lagrangian Equations
• Mathematics
• 2009
We prove the existence of non-smooth solutions to Special Lagrangian Equations in the non-convex case.
Hessian estimate for semiconvex solutions to the sigma-2 equation
• Mathematics
• 2019
We derive a priori interior Hessian estimates for semiconvex solutions to the sigma-2 equation. An elusive Jacobi inequality, a transformation rule under the Legendre–Lewy transform, and a mean valueExpand
Global solutions to special Lagrangian equations
We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.