Partial regularity of stable solutions to the fractional Gel'fand-Liouville equation

Abstract

We analyze stable weak solutions to the fractional Gel'fand problem \begin{equation*} (-\Delta)^su=e^u\quad\mathrm{in}\quad \Omega\subset\mathbb{R}^n. \end{equation*} We prove that the dimension of the singular set is at most $n-10s.$