I am looking for the proof of the following Theorem : Does anyone know where i can find out ?
If $\Omega$ is open and connected and $u_k$ be uniformly bounded sequence of harmonic functions . There exists a subsequence that converges uniformly to a harmonic function $u:\Omega \to \mathbb R$ on any compact subset of $\Omega$.
In case you think that its not hard, i look forward to hints as well.
I hope the statement is true .
Thanks.
Best Answer
See theorem 2.6 in the page 35 here and the comment below.