Strict convergence with equibounded area and minimal completely vertical liftings. (August 2022)

• Record Type: Journal Article
• Authors: Mucci, Domenico
• Is Part Of: Nonlinear analysis. Volume 221(2022)
• Publication Date: 2022-08
• Subjects: 49Q20 -- 49J45 -- 26B30; Lifting measures -- Functions of bounded variations -- Strict convergence -- Cartesian currents -- Relaxed area functional; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112943
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 B V . 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 lack of uniqueness in the high codimension case. Relationship with the relaxed area functional in the strict convergence is also discussed.