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arXiv · 2305.11299

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

Giovanni Bellettini·Simone Carano·Riccardo Scala
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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.

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Giovanni Bellettini, Simone Carano, Riccardo Scala. 2023-05-18. Relaxed area of graphs of piecewise Lipschitz maps in the strict $BV$-convergence. https://arxiv.org/abs/2305.11299

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