Calculus of Variations and Geometric Measure Theory

S. Carano

Relaxed area of $0$-homogeneous maps in the strict $BV$-convergence

created by carano on 16 Jun 2023
modified on 20 Feb 2024


Accepted Paper

Inserted: 16 jun 2023
Last Updated: 20 feb 2024

Journal: Annali di Matematica Pura ed Applicata
Pages: 16
Year: 2023


We compute the relaxed Cartesian area for general $0$-homogeneous map of bounded variation, with respect to the strict $BV$-convergence. In particular, we show that the relaxed area is finite for this class of maps and we provide an integral representation formula.

Keywords: relaxation, Plateau problem, area functional, strict convergence, total variation of the Jacobian, tangential variation