I have to solve the following PDE. We have that $f:\mathbb{R}^2 \rightarrow \mathbb{R}$ where
$$\lambda f - \frac{1}{2} \Delta f=0$$
with boundary conditions
\begin{align} \left(\frac{\partial f}{\partial x} - \frac{\partial f}{\partial y} \right)\Bigg|_{x=0} &= c_1 \\ \frac{\partial f}{\partial x} \Bigg|_{y=0} &= c_2 \\ \frac{\partial f}{\partial y} \Bigg|_{x=1} &= c_3 \end{align}
It doesn't matter which values the constants $c_1$ and $c_2$ have, but $c_3 > 0$ must be fixed.
Nothing I tried went in some useful direction, so I would be very glad if someone has an idea how to handle this problem.
Best Regards!