I'm taking an introductory level PDE class and for one lemma, we use the notion of regular boundary point, defined as follows: $\xi \in \partial \Omega$ is regular iff $\exists p $ superharmonic on $\Omega$ s.t. $p>0$ on $\overline{\Omega} \backslash \xi$ and $p(\xi)=0$.
I don't really know what this means; I couldn't tell you which type of boundary point is or isn't regular. I should also mention that if I'm not mistaken in this instance we use a generalized definition of a superharmonic funtion u which is that u satisfies $$ u(x)\leq \frac{1}{|\partial B_r(x)|}\int_{\partial B_r(x)} u(y) dS(y)$$ for all r small enough.
Edit: this is the definition for subharmonic, sorry