Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator

We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on ${\mathbb{R}}^N$, that is frequently hypercyclic with respect to the partial differentiation operator $\mathrm{\partial }\mathrm{/}\mathrm{\partial }{x}_k$ and which has a minimal growth rate in terms of the average $L^2$-norm on spheres of radius $r>0$ as $r\to \mathrm{\infty }$.