Hello. Thank you for taking the time for helping me. The following is the problem which I need to solve (there are actually two parts):
Please note that I am unable to use mathematical symbols (my computer does not allow me.) I will thus write out the following hints. For the first part of the problem we may consider log(R*/R) where R=|x-y|, R*=|x*-y|, with x* the mirror image of x=(x,y) with respect to y=0.
I have also know that the Poisson equation may be:
u(x,y) = [y divided by pi] times the integral (from negative infinity to positive infinity) of [u(m,o) divided by (m-x)squared + ysquared]dm.
I just need help deriving all of this. I have some idea but I cannot show you what I have (too complicated.) Thank you so much for taking the time in trying this question.
This shows how to construct Green's function for a given Dirichlet problem and derive Poisson's integral formula for the half plane.