My question refers to this answer. I was hoping someone could explain in more detail the following reasoning. It remains to observe that $\Delta v$ is the distribution composed of the ...
A professor I talked to showed me a proof of the mean value property. (He actually showed it for functions solving the heat equation instead of Laplace's equation, but it seems like the argument is ...
Let $H$ be the open half-space of $\Bbb R^n$ defined by $x_n > 0$. Let $f : \overline H \to \Bbb R$ continuous and harmonic on $H$. Define the function $F : \Bbb R^n \to \Bbb R$ by $$ ...