Calculus of Variations and Geometric Measure Theory

G. Crasta - V. De Cicco - A. Malusa

Pairings between bounded divergence-measure vector fields and BV functions

created by decicco on 16 Feb 2019
modified by malusa on 15 Jul 2020


Accepted Paper

Inserted: 16 feb 2019
Last Updated: 15 jul 2020

Journal: Adv. Calc. Var.
Year: 2020


We introduce a family of pairings between a bounded divergence-measure vector field A and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced by Anzellotti and Chen-Frid, all the main properties and features (e.g.\ coarea, Leibniz and Gauss-Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in BV. We remark that the standard pairing in general does not share this property.