I’m searching for a way to prove the Newtonian potential, given as a convolution in the form of:
$$ (E * Delta f)(x) = int_R E(x-y) Delta f(y) d^ny = f(x)$$
where $n=1$. Apparently this proof is supposed to be easy, but the only idea I have had is to use $x_o$ as the value and try and prove the formula $int E(x_o -y)Delta f(y) dy = f(x_o) = 0$, but really no clue if that’s a good way of doing it.
Any help on how to prove something like would be helpful! I’m quite confused as to how the $x-y$ part of the integral is supposed to be solved. I’m also not clear on how the E is supposed to be integrated.