Calculus of Variations and Geometric Measure Theory

G. Bellettini - S. Carano - R. Scala

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

created by carano on 12 Mar 2023
modified on 31 Oct 2023


Accepted Paper

Inserted: 12 mar 2023
Last Updated: 31 oct 2023

Journal: Nonlinear Analysis
Pages: 46
Year: 2023


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 $L^1$-relaxed area.

Keywords: relaxation, Plateau problem, area functional, Cartesian currents, strict convergence