Calculus of Variations and Geometric Measure Theory

G. Bellettini - A. Elshorbagy - R. Scala

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

created by scala on 03 Mar 2021
modified on 29 Mar 2021



Inserted: 3 mar 2021
Last Updated: 29 mar 2021

Year: 2021


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/
$, $x\neq0$, 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.