Related papers: Explicit gradient estimates for minimal Lagrangian…
We derive a priori interior Hessian and gradient estimates for special Lagrangian equation of phase at least a critical value in dimension three.
We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three…
We derive a priori interior Hessian estimates for the special Lagrangian equation $\sigma_{2}=1$ in dimension three.
We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interior gradient estimates for any constant phases.
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.
We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for…
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,…
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…
We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and the k-Hessian equation. By establishing uniform a priori…
In this paper, we establish a doubling argument to obtain Hessian estimates for the special Lagrangian equation under general phase constraints. In particular, our approach does not rely on the Michael-Simon mean value inequality. As an…
In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and…
In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient of the phase vanishes along its zero set. At the critical…
In this paper we study the {\it a priori} gradient estimates for admissible solutions to Neumann boundary value problem of fully nonlinear Hessian equations on Riemannian manifolds. We firstly derive an interior gradient estimates for…
We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for…
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
We derive a priori $C^2$ estimates for the $\chi$-plurisubharmonic solutions of general complex Hessian equations with right-hand side depending on gradients.
We derive second order estimates for $\chi$-plurisubharmonic solutions of complex Hessian equations with right hand sides depending on gradients on compact Hermitian manifolds.
In this paper, we derive a priori estimates for the gradient and second order derivatives of solutions to a class of Hessian type fully nonlinear parabolic equations with the first initial-boundary value problem on Riemannian manifolds.…
We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the…
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…