3 papers
math.AP2026
Giga-Kohn-type results for the fully fractional heat equation
Yannick Sire, Juncheng Wei, Ke Wu +1
We consider the semilinear fully fractional heat equation \[ (\partial_t-Î)^Ïu = |u|^{p-1}u \quad \text{in } \mathbb{R}^n \times \mathbb{R}_{-}, \qquad 0 < Ï< 1. \] For $n\leq 2…
math.AP2025
A Liouville theorem for supercritical Fujita equation and its applications
Kelei Wang, Juncheng Wei, Ke Wu
We prove a Liouville theorem for ancient solutions to the supercritical Fujita equation \[\partial_tu-Îu=|u|^{p-1}u, \quad -\infty <t<0, \quad p>\frac{n+2}{n-2},\] which says if $…
math.AP2025
Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface
Kelei Wang, Juncheng Wei, Ke Wu
We study properties of solutions to the fractional Allen-Cahn equation when and dimension . By applying the quantitative stratification principle developed…