Recently, I met an equation about the integration by parts and surface integrals. It says:$$
\int_{|\xi|\geq\epsilon}D_i\Gamma(\xi){\partial\over\partial{\xi_i}}f(\xi)d\xi=-\int_{|\xi|=\epsilon}D_i\Gamma(\xi)f(\xi){\xi_i\over{|\xi|}}dS$$
here $\Gamma$ satisfy $\triangle\Gamma(\xi)=0$ and $f\in C_0^\infty(R^n)$. So, is there someone that could explain it in detail?