Assume that $u\in W^{1,1}(\Omega)$, where $\Omega$ is a bounded domain in $\mathbb{R}^n$ having regular enough boundary (say Lipschitz). Then it is well known that also $u^+\in W^{1,1}(\Omega)$. Naturally, one could expect that $\mathrm{Tr}\, (u^+) = (\mathrm{Tr}\, u)^+$, but, to my surprise, I haven't found such a result in any book.

So I was wondering if this is true at all and if so, whether there is some reference for it.

Thank you very much for any help


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