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

2023/05/18 by Giovanni Bellettini, Bellettini, Giovanni, Simone Carano +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Topology and Set Theory #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2305.11299

openalex publication_date 2023/05/18 · openalex created_date 2023/05/23 · openalex updated_date 2026/07/28

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 L¹-relaxed area.

Cited by

• On the relaxation of polyconvex functionals with linear growth under strict convergence in BV

Related

• On the area of the graph of a piecewise smooth map from the plane to the\n plane with a curve discontinuity
• Relaxed area of 0-homogeneous maps in the strict BV-convergence
• Strict BV relaxed area of Sobolev maps into the circle: the high dimension case
• Solutions to the minimal surface system with large singular sets
• On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions