Yang Zhou

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20242026

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math.AP2025

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary

Jingbo Dou, Yazhou Han, Shuang Yuan +1

In this paper, we establish a sharp Onofri trace inequality on the upper half space $R_{+}^{n} (n \geq 2)$ by considering the limiting case of Sobolev trace inequalit…

math.AP2025

Liouville type theorem for a class of quasilinear p-Laplace type equations in the half space

Bao Yu, Yang Zhou

We use the method of vector fields to obtain a Liouville-type theorem for a class of quasilinear p-Laplace type equations with conormal boundary condition in the half space. These…

math.AP2025

Liouville theorem for subcritical nonlinear heat equation

Yang Zhou

We obtain a Li-Yau-type estimate for nonnegative ancient solutions to the subcritical semilinear heat equation $\frac{\p u}{\p t}=\De u+u^p$ in $\rz^n\times(-\infty,0)$. Then, we c…

math.AP2025

Global $C^{1, α}$ regularity for Monge-Ampère equations on planar convex domains

Qing Han, Jiakun Liu, Yang Zhou

In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation $det D^{2} u = f$ on strictly convex but not unifo…

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary

Liouville type theorem for a class of quasilinear p-Laplace type equations in the half space

Liouville theorem for subcritical nonlinear heat equation

Global C1,α regularity for Monge-Ampère equations on planar convex domains

Global $C^{1, α}$ regularity for Monge-Ampère equations on planar convex domains