Xiuda Liang

collaborators

3 papers

math.AP2026

Transformed Convexity for Lane--Emden Equations and Torsion on Spherical Domains

Xiuda Liang, Wenjie Wang

We study the geometry of positive Dirichlet solutions on smooth, uniformly geodesically convex domains $Ω ⊊ S^{n}$ , $n \geq 2$ . Set $p_{n}^{*} = 2 n / (2 n - 3)$ . For the Lane--Emden…

math.AP2026

Hessian degeneracy of the torsion function on smooth simply connected nonconvex planar domains

Xiuda Liang, Peng Luo, Wenjie Wang

We construct a family of bounded, smooth, simply connected, nonconvex planar domains $Ω_{a, ε}$ . Let $u_{a, ε}$ be the corresponding torsion function satisfying \[ -Δu_{a,ε}=1\quad\t…

math.AP2026

Precise asymptotic estimates and non-degeneracy of solutions to a biharmonic problem with large exponents in dimension four

Xiuda Liang, Wenjie Wang

We are concerned with the semilinear biharmonic problem under Dirichlet boundary conditions that \begin{equation*} \begin{cases} Δ^2 u=(u^+)^{p} &{\text{in}~Ω},\\[0.5mm] u \not\equ…