Hello everyone! Does anyone know if there is a know expression for the Green's function for Poisson's equation that vanishes on an ellipse in 2 dimensions? I'm essentially looking for a solution to: $$ \nabla^2G(\vec x-\vec x_0)=\delta^2(\vec x-\vec x_0) $$ in 2 dimensions where $$G(\vec x-\vec x_0)=0$$ when [itex]\vec x[/itex] lies on an ellipse. The solution for a circle is well know but I wanted to know if there any kind of generalization. Thanks a lot!