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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 . Let 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} Î^2 u=(u^+)^{p} &{\text{in}~Ω},\\[0.5mm] u \not\e…