Yang Zhou

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20242026

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3 papers · 2 filters

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…