Inserted: 24 mar 2022
Last Updated: 6 may 2022
Journal: Nonlinear Analysis
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Minimal lifting measures of vector-valued functions of bounded variation were introduced by Jerrard-Jung. They satisfy strong continuity properties with respect to the strict convergence in BV. Moreover, they can be described in terms of the action of the optimal Cartesian currents enclosing the graph of $u$. We deal with a good notion of completely vertical lifting for maps with values into the two dimensional Euclidean space. We then prove the lack of uniqueness in the high codimension case. The relationship with the relaxed area functional in the strict convergence is also discussed.
Keywords: Functions of Bounded Variations, Cartesian currents, lifting measures, strict convergence, relaxed area functional