Let be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its -homology group has notorsion. Weak limits of graphs of smooth maps with equibounded total variation give riseto equivalence classes of cartesian currents in for which we introduce a natural-energy.Assume moreover that the first homotopy group of iscommutative. In any dimension we prove that every element in can be approximatedweakly in the sense of currents by a sequence of graphs of smoothmaps with total variation converging to the-energy of . As a consequence, we characterize the lowersemicontinuous envelope of functions of bounded variations from into .
@article{ASNSP_2006_5_5_4_483_0,
author = {Giaquinta, Mariano and Mucci, Domenico},
title = {The $BV$-energy of maps into a manifold : relaxation and density results},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {483--548},
year = {2006},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {4},
zbl = {1150.49020},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2006_5_5_4_483_0/}
}
TY - JOUR AU - Giaquinta, Mariano AU - Mucci, Domenico TI - The $BV$-energy of maps into a manifold : relaxation and density results JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 483 EP - 548 VL - 5 IS - 4 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2006_5_5_4_483_0/ LA - en ID - ASNSP_2006_5_5_4_483_0 ER -
%0 Journal Article %A Giaquinta, Mariano %A Mucci, Domenico %T The $BV$-energy of maps into a manifold : relaxation and density results %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 483-548 %V 5 %N 4 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2006_5_5_4_483_0/ %G en %F ASNSP_2006_5_5_4_483_0
Giaquinta, Mariano; Mucci, Domenico. The $BV$-energy of maps into a manifold : relaxation and density results. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 483-548. https://www.numdam.org/item/ASNSP_2006_5_5_4_483_0/
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