I'm stuck on this problem I've been assigned in an electromagnetism class (it's a mathematical problem though).
Let . We define the spherical mean of as .
Demonstrate that if is a harmonic function (i.e. ) then u satisfies the equation for all .
Hint: Use .
According to my class notes, , where .
So I guess I should start with .
Now I'm not really sure how to proceed. I guess there's a trick with . I've been stuck here for days. I've seen the gradient appearing on the sheets of some people in my class, but I've no idea how I could introduce it.
Thanks for any help.