Let V be a harmonic and bounded function on $\mathbb{R}^2 \setminus \text{B}_R,\text{B}_R $ -- a ball with radius $R$. Proof that:
1) $\exists \lim\limits_{x \to \infty} V(x) $
2) $\nabla V(x) = \mathcal{O} \left( \frac{1}{|x|^2} \right), x \to \infty $.
Don't have any ideas. May somebody suggest something? Ideas?