Chapter 3Laplace’s Equation in Three Dimensions

• Properties of the three-dimensional 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).

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