Some Generalizations of the Boundary Value Problem with Oblique Derivative

Let $D$ be a two-dimensional domain bounded by a smooth closed contour $L$ and let $l$ be a smooth vector field on $L\setminus\Gamma$ where $\Gamma$ is finite. Using probability methods we investigate the bounded solutions of the boundary value problem $\Delta u=0$, $\frac{\partial u}{\partial l}\bigg|_{L\setminus\Gamma}=0$ and prove that they may be uniquely represented in form (2).