Find the two-dimensional solution to Laplace's equation inside an isosceles right triangle. The boundary conditions are as is shown in the picture:
The length of the bottom and left side of the triangle are both L.
From the image, it is clear that two of the boundary conditions are...
V(0,y) = 1
V(x,0) = 1
The Attempt at a Solution
My problem is getting started. I need more boundary conditions, but I am not sure how to get them. Also, I need use superposition or something to impose periodicity onto some part of this problem, but I can figure out how to do it. Also, another option is the zero option where X(x) = Y(y) = 0, but that doesn't seem to work either.
The only other boundary condition I can think of is V(x,L-x) = 0, but that doesn't seem to be enough information.
Can anyone help me get started with this problem? Thanks in advance.