Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn Equations

Changfeng Gui, Qinfeng Li

In this paper we study stable solutions to the fractional equation \begin{align} (-Δ)^s u =f(u), \quad |u| < 1 \quad \mbox{in ${\mathbb{R}}^d$}, \end{align}where $0<s<1$ and $f:[-1,1…