Consider some smooth function with compact support $\phi\in C^1_0(\Omega)$ where $\Omega\subset\mathbb{R}^n$ and furthermore some constant vector $c=(c_1,...,c_n)\in\mathbb{R}^n$. If I am not mistaken, then the Gauß Theorem should imply that $$\displaystyle\int_{\Omega}c\cdot D\phi(x) dx = 0$$ holds true, simply because $c$ is independent of $x$. Am I right? I just want to make sure I am not mistaken though. Thanks!
2026-03-28 08:48:20.1774687700
Gradient of smooth function vanishes
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