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Yes, indeed. The electrostatic potential $V$ satisfies $$\nabla^{2}V\left(\vec{r}\right)=-\frac{\rho\left(\vec{r}\right)}{\varepsilon_{0}}$$ so in a region $U\subset\mathbb{R}^{3}$ in which $\rho=0$, one also has $$\nabla^{2}V\left(\vec{r}\right)=0$$