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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…
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 \[\partial_tu-Δu=|u|^{p-1}u, \quad -\infty <t<0, \quad p>\frac{n+2}{n-2},\] which says if $u…