Let \(\Omega\subseteq \mathbb{R}^d\) be an open subset with \(C^1\)-boundary . If \(u\in C^1(U)\) where \(U\) is an open neighbourhood of \(\bar{\Omega}\), then
\[ \int_{\Omega} \nabla u=\int_{\partial \Omega} u\nu , \]where \(\nu\) is the outward normal vector to \(\partial \Omega\).
This is the so called divergence theorem or Gauss’s theorem.