How to prove the following inequality between $u$ and integral of its gradient I'm reading a paper and it states that the following result is well known.
I can't prove it myself but would like to see a proof before I continue the reading, can anybody help?

$\text{Let}\ u\in C_0^{\infty}(B_R(x))\ \text{where}\ B_R(x)\ \text{is a ball of radius}\ R\ \text{centered at}\ x\ \text{then}$
$$|u(x)| \leq c \int_{B_{R}(x)} \frac{|\nabla u(y)|}{|x-y|^{n-1}} d y$$


Hints:

*

*Consider what is given by the divergence theorem, about the integral $\iiint \nabla f$ performed over a ball centered at $x$ with radius $r\leq R$

*Consider how the surface area of the previous ball scales with $r$

*Apply the triangle inequality

