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Let $\Omega$ be connected bounded open set in $\mathbb{R}^{n}$. Let $U:\Omega\rightarrow \mathbb{R}^{n}$ be a $C^{1}$ vector field. The divergence theorem is given \begin{align} \int_{\Omega} \nabla\cdot U\,\mathrm{dx}=\int_{\partial\Omega} U\cdot\nu \mathrm{ds} \end{align}

I would like to know if there exists a similar theorem like divergence theorem which can change the following integrals to be on the boundary integrals \begin{align} \int_{\Omega} V\cdot\nabla U\,\mathrm{dx}\quad \text{and}\quad \int_{\Omega} RU\,\mathrm{dx} \end{align} where $R$ is a constant

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    $\begingroup$ What is $RU$? the curl of $U$? $\endgroup$ – Rafa Budría Mar 19 at 10:57

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