Definition 3.1.2831D179000C4D

Definition 3.1.28.31D179000C4D A boundary point $\xi \in \partial \Omega $ is regular if $U_ f(x)\to f(\xi )$ as $\Omega \ni x\to \xi $, for every $f\in C(\partial \Omega )$. A barrier at $\xi $ is a positive continuous supersolution $b$ on $\Omega $ such that $b(x)\to 0$ as $x\to \xi $ and, for every neighborhood $N$ of $\xi $ with $\Omega \setminus N\neq \varnothing $,