For harmonic function $u\in C^2(B_r(0))\cap C(\overline B_r(0)),$ is there a sequence of harmonic functions $u_n\in C^2(B_r(0))\cap C^1(\overline B_r(0))$ such that $u_n \to u$ in $C(\overline B_r(0))$? Here $ B_r(0)$ is an open ball centered at $0$ with radius $r$.
I would be grateful if you give any comment for this question. Thanks in advance!