I want to solve the following problem.
We have a triangle with side lengths $a,b,c$.
We have a potential inside the triangle satisfying the 2D wave equation with source at $(x_0,y_0)$ which is $\partial^2_x \phi(x,y)+ \partial^2_y \phi(x,y) = \delta(x-x_0,y-y_0)$.
With boundary conditions that $\phi(x,y)=0$ on the boundary of the triangle.
Is there a solution to this basic problem somewhere in the literature?
I have a feeling it should be solved using elliptic functions.(At least I think this is true for special cases such as when the triangle is equilateral).