Let $\Phi : \mathbb{R}^n \setminus \{0\} \to \mathbb{R}$ be the fundamental solution to Laplace’s equation defined by
\begin{align*}
\Phi(x) :=
\begin{cases}
-\dfrac{1}{2\pi} \log |x| & \text{if } n = 2, \\
\dfrac{1}{n(n - 2)\alpha(n)} \cdot \dfrac{1}{|x|^{n - 2}} & \text{if } n \geq 3,
\end{cases}
\end{align*}
where $\alpha(n)$ denotes the volume of the unit ball in $\mathbb{R}^n$. Then, as a [distribution](/page/Distribution) on $\mathbb{R}^n$,
\begin{align*}
\Delta \Phi = \delta_0,
\end{align*}
where $\delta_0$ is the Dirac delta distribution at the origin.
