Ruosi Chen

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20232026

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4 papers · 1 filter

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…

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

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