Special Session 107: Recent advances in regularity theory for local and nonlocal elliptic and parabolic equations
Liouville-type theorems for nonlocal Lane--Emden inequalities via test function methods
Taehun Lee
Konkuk University Korea
Co-Author(s): Takwon Kim
Abstract:
We present Liouville-type theorems for nonnegative weak supersolutions of nonlocal Lane--Emden inequalities driven by integro-differential operators of order $2s$ with $s\in(0,1)$. In the linear setting, we consider $L_K u = u^q$ in $\mathbb{R}^n$, where $K$ is an even, uniformly elliptic kernel, and prove that $u\equiv 0$ for $1