which implies that in and hence in . Thus, for a harmonic function in , if either
In particular, if as is continuous, then
----------(77)
then, in also. As a particular case, if are two harmonic function in such that on , then satisfies equations (77), and hence in i.e., in
Thus, a harmonic function in uniquely determined by its values on the boundary of We close this section by giving some examples of harmonic functions.
Examples of harmonic functions:
The flow of heat in a body : The equation governing the heat flow is
in 
and hence 
in 
. Thus, for a harmonic
function in 
, if either 
is continuous, then 
----------(77) 
in 
also. As a particular case, if 
are two harmonic function in 
such that 
on 
, then 
satisfies equations (77), and hence 
in 
i.e., 
in 
uniquely determined by its values on the boundary of 
We close this section by giving some examples of harmonic functions. 
