Let $U$ be a non-empty bounded open set of $\mathbb{R}^n$ ($n \geqslant 2$). Let $f$ be a function continuous on $\bar{U}$, of class $\mathcal{C}^2$ and harmonic on $U$. For all $\varepsilon > 0$ we set $g_\varepsilon(x) = f(x) + \varepsilon \|x\|^2$. Show that $g_\varepsilon$ is a function continuous on $\bar{U}$, of class $\mathcal{C}^2$ on $U$, and such that $\forall x \in U, \Delta g_\varepsilon(x) > 0$.