相关论文: Quadratic Hessian equation

We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.

In this paper, we prove the existence of viscosity solutions to complex Hessian equations on compact Hermitian manifolds, assuming the existence of a strict subsolution in the viscosity sense. The results cover the complex Hessian quotient…

This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…

In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.

We prove that viscosity solutions to the quadratic Hessian equation $$\sigma_2(D^2u) = 1$$ cannot touch a harmonic function on a minimal surface from below. This can be viewed as a form of strict $2$-convexity. We also prove an a priori…

We study a general class of quadratic BSDEs with terminal value in Lp for p > 1. First of all, we give an Lp-type estimate and existence result. Under the additional assumption of monotonicity and convexity, we derive the comparison…

In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed…

We prove that all entire smooth strictly convex self-shrinking solutions on $\mathbb{R}^n$ to the Hessian quotient flows must be quadratic. This generalizes the rigidity theorem for entire self-shrinking solutions to the Lagrangian mean…

A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in $\C^n$. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by…

The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two numerical methods for this PDE: the first is provably…

The curvature estimates of $k$ curvature equations for general right hand side is a longstanding problem. In this paper, we totally solve the $n-1$ case and we also discuss some applications for our estimate.

In this paper, we shall study existence of weak solutions to complex Hessian equations. With appropriate assumptions, it is possible to obtain weak solutions in pluripotential sense.

We obtain a prior $C^{1,1}$ estimates for some Hessian (quotient) equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior $C^{2,\alpha}$ regularity for $C^0$…

We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.

In this work we derive global estimates for viscosity solutions to fully nonlinear elliptic equations under relaxed structural assumptions on the governing operator which are weaker than convexity and oblique boundary conditions and under…

We show that in dimension 3 axial-symmetric viscosity solutions of uniformly elliptic Hessian equations are in fact the classical ones.

We prove that convex viscosity solutions to the quadratic Hessian inequality $\sigma_2(D^2u) \geq 1$ are strictly $2$-convex. As a consequence we obtain short proofs of smoothness and interior $C^2$ estimates for convex viscosity solutions…

We consider viscosity solutions of a class of nonlinear degenerate elliptic equations on bounded domains. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many…

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…

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…