Let \(U\) be bounded, open, and \(\partial U \in C^1\). Then for \(u, v \in C^2(\overline{U})\) the Green’s formula holds
\[ \int_U u \Delta v - v \Delta u = \int_{\partial U} u \nabla_\nu v - v \nabla_\nu u. \]Let \(U\) be bounded, open, and \(\partial U \in C^1\). Then for \(u, v \in C^2(\overline{U})\) the Green’s formula holds
\[ \int_U u \Delta v - v \Delta u = \int_{\partial U} u \nabla_\nu v - v \nabla_\nu u. \]