Fundamental Solution of N-Dimensional Laplace equation

Please see the attached.

The fundamental solution of the n-dimensional Laplace equation solves

, (1)

where   is the n-dimensional delta function.  

a.  Show that if  , the solution of the above equation (1) for   is

,

where   is a constant.

b.   Use the n-dimensional Gauss theorem to evaluate the left hand side of the equation (1) and show that



where   is the surface area of the n-dimensional unit sphere defined by

  

Note the singularity for n = 2.

Attached file(s):

PDE4.2.doc  View File