Suppose $\Omega\subseteq \mathbb C^n, n>1,$ is a bounded domain and $K=\overline \Omega$ is its closure. The Newton potential of the Lebesgue measure $\lambda$ restricted to $K$ is defined as $$u(z)=\int_{K}\frac{1}{\Vert z-\zeta\Vert^{2n-2}} d\lambda (\zeta).$$
A well-known fact is that $-u$ is subharmonic on $\mathbb C^{n}$ but can not be globally plurisubharmonic since it is bounded above. My question is about the plurisubharmonicity of $-u$ on $\Omega$.
Under what assumptions on the domain is $-u$ plurisubharmonic on $\Omega$?
In one of the rare cases when the Newton potential can be computed explicitly, namely when $\Omega$ is the ball, $-u$ takes the form $C_1\Vert z\Vert^2+C_2$ on $\Omega$, so it is plurisubharmonic there.