solving the Laplace equation I want to know that:
 What is the general solution of the (2 and 3 dimentional)Laplace equation $f_{xx}+ f_{yy}=0$ and $f_{xx}+ f_{yy} +f_{zz}=0$?
How can we solve the Laplace equation?
With many thanks for your help.

You can find more information here: https://en.wikipedia.org/wiki/Fundamental_solution but to give you an intuition to how it is solved, the Laplace operator is translation invariant, so you seek a solution $g(r)=f(x)$ where $r=|x|$, and plug this into the PDE, this gives you a second order ODE, solving this gives the fundamental solution.
