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.
Bellettini, G., Carano, S., Scala, R. (2024). Relaxed area of graphs of piecewise Lipschitz maps in the strict BV-convergence. NONLINEAR ANALYSIS, 239, 1-33 [10.1016/j.na.2023.113424].
Relaxed area of graphs of piecewise Lipschitz maps in the strict BV-convergence
Giovanni Bellettini;Riccardo Scala
2024-01-01
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.
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https://hdl.handle.net/11365/1250214