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

[BibTeX]

Preprint

Inserted: 12 mar 2023
Last Updated: 12 mar 2023

Pages: 46
Year: 2023

Abstract:

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


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