6 papers
Small-energy regularity for stationary weak solutions of the Liouville equation
Haotong Fu, Kelei Wang, Wei Wang +1
We establish small-energy regularity for stationary weak solutions of the Liouville equation in every dimension. It solves a problem left open in Da Lio [Commun. Partia…
Stable De Giorgi conjecture of the Allen--Cahn equation in
Yong Liu, Tianci Luo, Kelei Wang +3
We prove that every bounded stable entire solution of the Allen--Cahn equation in is one-dimensional. As a consequence, the full De Giorgi conjecture in i…
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…
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…
F-stability, entropy and energy gap for supercritical Fujita equation
Kelei Wang, Juncheng Wei, Ke Wu
We study some problems on self similar solutions to the Fujita equation when , especially, the characterization of constant solutions by the energy. Motivated by rec…
On Dancer's conjecture for stable solutions with sign-changing nonlinearity
Yong Liu, Kelei Wang, Juncheng Wei +1
We establish a Liouville type result for stable solutions for a wide class of second order semilinear elliptic equations in with sign-changing nonlinearity . Un…