Affiliation:
1. Dipartimento di Matematica “G. Castelnuovo” , Sapienza Università di Roma , P.le A. Moro 5, 00185 Roma , Italy
2. Dipartimento di Scienze di Base e Applicate per l’Ingegneria , Sapienza Università di Roma , Via A. Scarpa 10, 00185 Roma , Italy
Abstract
Abstract
We introduce a family of pairings between a bounded divergence-measure vector field 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 in [G. Anzellotti,
Pairings between measures and bounded functions and compensated compactness,
Ann. Mat. Pura Appl. (4) 135 1983, 293–318], [G.-Q. Chen and H. Frid,
Divergence-measure fields and hyperbolic conservation laws,
Arch. Ration. Mech. Anal. 147 1999, 2, 89–118], 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
\mathrm{BV}
.
We remark that
the standard pairing in general does not share this property.
Subject
Applied Mathematics,Analysis
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