Yang Zhou

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20242026

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9 papers · 1 filter

math.AP2026

Singular Extremal Solutions on Thin Ellipsoids with Varying Nonlinearities

Bao Yu, Yang Zhou

Let $N = m + 1$ and consider the thin ellipsoid \[ Ω_\varepsilon=\{(y,x_N)\in\mathbb R^m\times\mathbb R:\ |y|^2+\varepsilon^{-2}x_N^2<1\}. \] We prove that in every sufficiently large…

math.AP2026

Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality

Bao Yu, Yang Zhou

Let $n \geq 3$ and $1 < p < n$ . We first prove the local trace analogue of the sharp one-bubble critical-point stability theorem of Liu and Zhang~\cite{LiuZhang2025}: near a positive trac…

math.AP2026

Uniqueness for the Degenerate Monge-Ampère Equation on Arbitrary Bounded Convex Domains

Yang Zhou

Let $n \geq 2$ and let $Ω \subset R^{n}$ be an arbitrary bounded open convex set. The author prove that, for $p > n$ , the Dirichlet problem \[ \det D^2u=(-u)^p\quad\text{in }Ω, \qqu…

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…

math.AP2024

A priori estimates for parabolic Monge-Ampère type equations

Yang Zhou, Ruixuan Zhu

We prove the existence and regularity of convex solutions to the first initial-boundary value problem for the parabolic Monge-Ampère equationn $$ \left\{\begin{eqnarray} &&-u_t+\de…

math.AP2024

Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality

Yang Zhou

We consider the Euler-Lagrange equation of Sobolev trace inequality and prove several classification results. Exploiting the moving sphere method, it has been shown, when $p = 2$ , po…

Singular Extremal Solutions on Thin Ellipsoids with Varying Nonlinearities

Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality

Uniqueness for the Degenerate Monge-Ampère Equation on Arbitrary Bounded Convex Domains

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

A priori estimates for parabolic Monge-Ampère type equations

Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality

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