Passage of Evans' proof of the mean-value property of the heat equation On page 54 of the Evans for PDE, it states
$$\frac{1}{t^n} \iint _{E(t)} \frac{|y|^2}{s^2} \,dy\,ds = \iint_{E(1)}\frac{|y|^2}{s^2} \,dy\,ds = 4$$
saying "We omit the details of this last computation."
I'd love the details though.. I tried integrating myself but I have problems with integrals in $R^n$. Can anyone help me?
Set $E$:
$$E(x,t;r):= \left\{ (y,s)\in R^{n+1}\mid s\le t,\Phi(x-y,t-s) \ge \frac{1}{r^n} \right\}$$
Where $\Phi$ is the fundamental solution of the heat equation:
$$\Phi(x,t)=\frac{1}{(4 \pi t)^{n/2}}e^{-\frac{|x|^2}{4t}} \text{ with } t>0.$$
When he states $E(t)$ he means the other two variables, $x$ and $r$, are zero.
The entire proof is here at page 10, http://math.uchicago.edu/~may/REU2014/REUPapers/Ji.pdf , what I'm referring to is at page 11.

Found the answer How to prove that $\iint\frac{|y|^2}{s^2}\,dy\,ds=4$?
I thought I had searched well enough, seems like I didn't. Sorry for the trouble
