The $L^1$-relaxed area of the graph of the vortex map: optimal upper bound

Giovanni Bellettini, Alaa Elshorbagy, Riccardo Scala

We compute an upper bound for the value of the $L^1$-relaxed area of the graph of the vortex map $u:B_l(0)\subset {\mathbb{R}}^2\to {\mathbb{R}}^2$, $u(x):=x/|x|$, $x \neq 0…