Yasheng Lyu

collaborators

4 papers

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., $sup I^ u < \infty$ ) and the Christoffel-Minkowski equation admits $C^{1, 1}$ regularity und…

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 HÃ¶lder estimates for the gradient of quasilinear elliptic equations

Dongsheng Li, Yasheng Lyu

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

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 HÃ¶lder estimates for the gradient of quasilinear elliptic equations

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