Cheuk-Yan Fung

activity

20212026

collaborators

Showing 2026Show all

2 papers · 1 filter

math.AP2026

Doubling Argument of the Hessian Estimate for the Hessian Quotient Equations

Cheuk Yan Fung

In this paper, we establish a doubling argument to obtain Hessian estimates for convex solutions to the Hessian quotient equation $\frac{σ _{n}}{σ _{k}} (D^{2} u) = f (x, u, D u)$ for $k = n - 1$ an…

math.AP2026

On Counterexamples to Interior $C^{2}$ Estimates for Monge-Ampère Type Equations

Cheuk Yan Fung

We modify Pogorelov's classic construction to demonstrate the absence of a priori $C^{2}$ estimates for the equations $det (D^{2} u \pm D u \otimes D u) = f (x)$ in dimension $n \geq 3$ . W…

Doubling Argument of the Hessian Estimate for the Hessian Quotient Equations

On Counterexamples to Interior C2 Estimates for Monge-Ampère Type Equations

On Counterexamples to Interior $C^{2}$ Estimates for Monge-Ampère Type Equations