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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solution of laplace equation in the quarter plane

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**