Chapter 3Laplace’s Equation in Three Dimensions
Properties of the threedimensional Laplace equation:
 V(x,y,z) is the average of V around this point:





where R is the radius of the sphere centered around (x,y,z) used in the evaluation of the surface integral.
 The solution of Laplace's equation can not have local maxima or minima. Extreme values must occur at the end points (the boundaries).