The $L^1$-relaxed area of the graph of the vortex map

Giovanni Bellettini, Alaa Elshorbagy, Riccardo Scala

We compute the value of the $L^1$-relaxed area of the graph of the map $u:B_l(0)\subset {\mathbb{R}}^2\mapsto {\mathbb{R}}^2$, $u(x):=x/|x|$, $x\ne 0$, for all values of $…