Laplace And Poisson Equations

LAPLACE AND POISSON EQUATIONS

The purpose of this chapter is to study the two dimensional equation

u(x; y) uxx(x; y) + uyy(x; y) = f(x; y); (x; y) 2 R2

and its higher dimensional version

u uxx + uyy + uzz = f(x; y; z); (x; y; z) 2 R3: When f 0 in the domain the homogeneous equation is called the

Laplace equation. The nonhomogeneous equation usually is called the Poisson equation.