Hi, I need some help with the following problem:
Let $u(x_0,y_0)$ be a point of the boundary of a domain $\Omega$ contained in a circle of radius $R$ with center at $(x_0,y_0)$. Let $u$ be an harmonic function in $\Omega$, and continuous in $\Omega \cup \partial \Omega$ except in $(x_0,y_0)$. Demonstrate that if $ \frac{u(x,y)}{\log \left( { {2R^2}\over{(x-x_0)^2+(y-y_0)^2} } \right)} \longrightarrow 0 $ when $u(x,y)$ tends to $u(x_0,y_0)$, then $u\leq M$ in omega.
Thank you for your help :)