Relaxed area of graphs of piecewise Lipschitz maps in the strict BV-convergence

We compute the relaxed Cartesian area in the strict BV-convergence on a class of piecewise Lipschitz maps from the plane to the plane, having jump made of several curves allowed to meet at a finite number of junction points. We show that the domain of this relaxed area is strictly contained in the domain of the classical L1-relaxed area.

Automated summary

This article computes the relaxed Cartesian area in the strict BV-convergence for a class of piecewise Lipschitz maps from the plane to the plane, where the jump is composed of multiple curves that are allowed to meet at a finite number of junction points. It is shown that the domain of this relaxed area is strictly contained within the domain of the classical L1-relaxed area.