Solution of laplace equation in the quarter plane

1. Mar 13, 2007

catcherintherye

I am required to use the fourier transform to show that the solution of laplace gradF=0, in the quarter plane x>=0, y>=0 with b.c.'s F(x,y)->0 as xsqd + ysqd ->inf, partialH by x =0 on x=0 and H(x,y)=1/(1+xsqd) on y=0. Is (1+y)/(x^2+(1+y)^2). I have no idea about how to approach this problem.

I have a similar problem solved in the half plane, y>=0, -inf<x<+inf, with b.c's H(x,0)=f(x) (arbitrary), H->0 as (x^2+y^2)^1/2.

This solution starts by taking F.T in the x direction, to derive transform Hyy-k^2transformH=0 (yy denotes twice partial derivative of H w.r.t y) is this the same as in question 1?