Let $U$ be a connected and bounded Domain, w.l.o.g. we choose $[0,1]^2$ and let $f \in \mathcal{C}^2((0,1)^2)$ with $\Delta f(x)=0$ for $x \in (0,1)^2$ and having normal derivative of $0$ almost everywhere on the boundary with respect to the surface measure. Furthermore define $X_t$ to be a process which behaves like the standard Brownian Motion in $(0,1)^2$ and has normal reflection on the boundary (the classical reflected brownian motion)