*Preprint*

**Inserted:** 3 mar 2021

**Last Updated:** 29 mar 2021

**Year:** 2021

**Abstract:**

We compute the value of the $L^1$-relaxed area of the graph of the map $u:B_l(0)\subset\mathbb R^2\rightarrow\mathbb R^2$,
$u(x):= x/

x

$, $x\neq0$, for all values of $l>0$. Interestingly, for $l$ in a certain range, in particular
$l$ not too large, a Plateau-type problem, having as solution a sort of catenoid constrained to
contain a segment, has to be solved.

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