On the logarithmic potential defined for a Van Koch curve

This is a continuation of [1]. Under study are the differentiability properties of the logarithmic potential determined for some class of complex measures distributed on Van Koch's curves. Unlike the classical case of regular curves, the potential is shown to be of class $C^1$ on the whole plane $\mathbb C$. We also study a related analog of Robin's problem. The proofs are based on some results of [1].