Ruosi Chen

activity

20232026

collaborators

7 papers

math.AP2026

Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase

Ruosi Chen, Xingchen Zhou, Ruixuan Zhu

Let $n \geq 3$ . We prove a priori interior gradient estimate for the Lagrangian mean curvature equation \[ \sum_{i=1}^n\arctanλ_i(D^2u)=θ(x) \] under the critical and supercritical ph…

math.AP2026

Interior $C^{2, α}$ Regularity for the Quadratic Hessian Equation

Ruosi Chen, Xingchen Zhou, Ruixuan Zhu

We establish interior $C^{2, α}$ regularity for admissible solutions of the quadratic Hessian equation with positive $C^{α}$ right-hand side on the full positive branch. The main ingr…

math.AP2026

Regularity for convex viscosity solutions of $σ_{3}$ equation

Ruosi Chen, Yannan Liu, Xingchen Zhou

We prove interior $C^{2}$ regularity for convex viscosity solutions of the $3$ -Hessian equation $σ_{3} (D^{2} u) = f (x)$ with $f \in C^{0, 1}, in f f > 0$ , under a strict $3$ -convexity condition…

math.AP2026

Regularity for convex viscosity solutions of $σ_{2}$ Equation

Ruosi Chen, Huaiyu Jian, Xushan Tu +1

We prove interior $C^{2}$ regularity result for convex viscosity solutions of the quadratic Hessian equation $σ_{2} (D^{2} u) = f (x)$ , under the assumption that $f \in C^{0, 1}$ with $\inf…

math.AP2024

New Approach for Interior Regularity of Monge-Ampère Equations

Ruosi Chen, Xingchen Zhou

By developing an integral approach, we present a new method for the interior regularity of strictly convex solution of the Monge-Ampère equation $det D^{2} u = 1$ .

math.AP2024

An Integral Approach to Prescribing Scalar Curvature Equations

Ruosi Chen, Huaiyu Jian, Xingchen Zhou

We develop an integral approach to obtain interior a priori $C^{1, 1}$ estimates for convex solutions of prescribing scalar curvature equations $σ_{2} (κ) = f (x)$ as well as the Hessia…

math.AP2023

The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Ampère Equations

Ruosi Chen, Huaiyu Jian

We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge-Ampère Equations: one is singular which is from the proper affine hypersphe…

Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase

Interior C2,α Regularity for the Quadratic Hessian Equation

Regularity for convex viscosity solutions of σ3​ equation

Regularity for convex viscosity solutions of σ2​ Equation

New Approach for Interior Regularity of Monge-Ampère Equations

An Integral Approach to Prescribing Scalar Curvature Equations

The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Ampère Equations

Interior $C^{2, α}$ Regularity for the Quadratic Hessian Equation

Regularity for convex viscosity solutions of $σ_{3}$ equation

Regularity for convex viscosity solutions of $σ_{2}$ Equation