Yasheng Lyu

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math.AP2026

On the Dirichlet problem for the degenerate $2$ -Hessian equation

Yasheng Lyu

In this paper, we establish global $C^{1, 1}$ solvability of the Dirichlet problem for the degenerate $2$ -Hessian equation on bounded strictly mean convex $C^{3, 1}$ domains $Ω$ , wit…

math.AP2026

Global $W^{2, p}$ and $C^{2, α}$ regularity for the sigma- $2$ equation

Yasheng Lyu

In this paper, we prove that continuous $2$ -convex solutions of the $σ_{2}$ equation with positive continuous density on bounded strictly mean-convex $C^{3}$ domains with $C^{3}$ b…

math.AP2026

Interior $W^{2, p}$ regularity for the sigma- $2$ equation

Yasheng Lyu

We prove that continuous $2$ -convex solutions of the $σ_{2}$ equation with a density bounded above and below by positive constants belong to $W_{loc}^{2, 1}$ in every dimen…

math.AP2026

Second-order estimates for degenerate complex $k$ -Hessian and Christoffel-Minkowski equations

Yasheng Lyu

It is known that the complex $k$ -Hessian equation admits almost $C^{1, 1}$ regularity (i.e., $sup Δ u < \infty$ ) and the Christoffel-Minkowski equation admits $C^{1, 1}$ regularity unde…

math.AP2026

Remarks on the Pogorelov type estimate for the degenerate $k$ -Hessian equation

Yasheng Lyu

This paper investigates the Pogorelov type estimate for the $k$ -Hessian equation under a new condition on the degenerate right-hand side $f$ .

math.AP2025

On the Dirichlet problem for the degenerate $k$ -Hessian equation

Yasheng Lyu

This paper investigates the existence of a global $C^{1, 1}$ solution to the Dirichlet problem for the $k$ -Hessian equation with a nonnegative right-hand side $f$ , focusing on the r…

math.AP2025

A new proof of Hölder estimates for the gradient of quasilinear elliptic equations

Dongsheng Li, Yasheng Lyu

In this paper, we give a new proof of Hölder estimates for the gradient of quasilinear elliptic equations, using a covering method inspired by the proof of Evans-Krylov theorem for…

On the Dirichlet problem for the degenerate 2-Hessian equation

Global W2,p and C2,α regularity for the sigma-2 equation

Interior W2,p regularity for the sigma-2 equation

Second-order estimates for degenerate complex k-Hessian and Christoffel-Minkowski equations

Remarks on the Pogorelov type estimate for the degenerate k-Hessian equation

On the Dirichlet problem for the degenerate k-Hessian equation

A new proof of Hölder estimates for the gradient of quasilinear elliptic equations

On the Dirichlet problem for the degenerate $2$ -Hessian equation

Global $W^{2, p}$ and $C^{2, α}$ regularity for the sigma- $2$ equation

Interior $W^{2, p}$ regularity for the sigma- $2$ equation

Second-order estimates for degenerate complex $k$ -Hessian and Christoffel-Minkowski equations

Remarks on the Pogorelov type estimate for the degenerate $k$ -Hessian equation

On the Dirichlet problem for the degenerate $k$ -Hessian equation