Rui-Xuan Zhu

collaborators

3 papers

math.AP2026

Rigidity for Convex Entire Solutions to the $k$ -Hessian Equation

Xingchen Zhou, Ruixuan Zhu

We prove that for each $3 \leq k \leq n - 1$ a convex $C^{2}$ entire solution of $σ_{k}$ equation in $R^{n}$ with positive constant right hand side is a quadratic polynomial, without…

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

Interior $C^{2, α}$ Regularity for Convex Solutions of the 2-Hessian Equation

Xingchen Zhou, Ruixuan Zhu

We consider convex admissible viscosity solutions of $σ_{2} (D^{2} u) = f > 0$ in an open subset of $R^{n}$ , where $n \geq 2$ , $0 < α < 1$ , and $f \in C_{loc}^{0, α}$ . We prove that ev…

Rigidity for Convex Entire Solutions to the k-Hessian Equation

Interior C2,α Regularity for the Quadratic Hessian Equation

Interior C2,α Regularity for Convex Solutions of the 2-Hessian Equation

Rigidity for Convex Entire Solutions to the $k$ -Hessian Equation

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

Interior $C^{2, α}$ Regularity for Convex Solutions of the 2-Hessian Equation